Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The equation of the hyperbola whose foci are (6, 4) and (–4, 4) and eccentricity 2 is given by

$12 x^{2} - 4 y^{2} - 24 x + 32 y - 127 = 0$
$12 x^{2} + 4 y^{2} + 24 x - 32 y - 127 = 0$
$12 x^{2} - 4 y^{2} - 24 x - 32 y + 127 = 0$
$12 x^{2} - 4 y^{2} + 24 x + 32 y + 127 = 0$

The correct answer is: $12 x to the power of 2 end exponent minus 4 y to the power of 2 end exponent minus 24 x plus 32 y minus 127 equals 0$

Foci are (6,4) and (–4,4), $e equals 2$ and centre is $open parentheses fraction numerator 6 minus 4 over denominator 2 end fraction comma 4 close parentheses equals left parenthesis 14 right parenthesis$
Þ $6 equals 1 plus a e$ Þ $a e equals 5$ Þ $a equals fraction numerator 5 over denominator 2 end fraction$ and $b equals fraction numerator 5 over denominator 2 end fraction left parenthesis square root of 3 right parenthesis$
Hence the required equation is $fraction numerator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent over denominator left parenthesis 25 divided by 4 right parenthesis end fraction minus fraction numerator left parenthesis y minus 4 right parenthesis to the power of 2 end exponent over denominator left parenthesis 75 divided by 4 right parenthesis end fraction equals 1$
or $12 x to the power of 2 end exponent minus 4 y to the power of 2 end exponent minus 24 x plus 32 y minus 127 equals 0$ .

Related Questions to study

Mg and Li are similar in their properties due to

Mg and Li are similar in their properties due to

Chemistry-General

When an electron makes a transition from $left parenthesis n plus 1 right parenthesis$ state to $n$ state, the frequency of emitted radiations is related to $n$ according to $left parenthesis n much greater-than 1 right parenthesis$

When an electron makes a transition from $left parenthesis n plus 1 right parenthesis$ state to $n$ state, the frequency of emitted radiations is related to $n$ according to $left parenthesis n much greater-than 1 right parenthesis$

Chemistry-General

The binding energy of an element is 64 Mev. If BE/nucleon is 6.4, then the number of nucleons are

The binding energy of an element is 64 Mev. If BE/nucleon is 6.4, then the number of nucleons are

Chemistry-General

parallel

The ionization potential hydrogen atom is $13.6 blank e V$ . The energy required to remove an electron in the $n equals 2$ state of the hydrogen atom is

The ionization potential hydrogen atom is $13.6 blank e V$ . The energy required to remove an electron in the $n equals 2$ state of the hydrogen atom is

Chemistry-General

In nuclear reaction, $blank subscript 3 end subscript superscript 7 end superscript L i plus blank subscript 1 end subscript superscript 1 end superscript H rightwards arrow 2 blank subscript 2 end subscript superscript 4 end superscript H e$ The mass loss is nearly 0.02 amu. Hence, the energy released (in units of million kcal/mol) in the process is approximately

In nuclear reaction, $blank subscript 3 end subscript superscript 7 end superscript L i plus blank subscript 1 end subscript superscript 1 end superscript H rightwards arrow 2 blank subscript 2 end subscript superscript 4 end superscript H e$ The mass loss is nearly 0.02 amu. Hence, the energy released (in units of million kcal/mol) in the process is approximately

Chemistry-General

There are $0.618 blank mu g blank$ of $blank to the power of 206 end exponent P b$ and $0.238 blank mu g blank$ of $blank to the power of 238 end exponent U$ in a rock. If $T subscript 50 end subscript$ of $blank to the power of 238 end exponent U$ is $1.5 cross times 10 to the power of 9 end exponent y r comma$ age of the rock is

There are $0.618 blank mu g blank$ of $blank to the power of 206 end exponent P b$ and $0.238 blank mu g blank$ of $blank to the power of 238 end exponent U$ in a rock. If $T subscript 50 end subscript$ of $blank to the power of 238 end exponent U$ is $1.5 cross times 10 to the power of 9 end exponent y r comma$ age of the rock is

Chemistry-General

parallel

The latus-rectum of the hyperbola $16 x to the power of 2 end exponent minus 9 y to the power of 2 end exponent equals$ $144$ , is

The latus-rectum of the hyperbola $16 x to the power of 2 end exponent minus 9 y to the power of 2 end exponent equals$ $144$ , is

Let $stack a with rightwards arrow on top equals 2 stack i with hat on top plus stack j with hat on top minus 2 stack k with hat on top$ and $stack b with rightwards arrow on top equals stack i with hat on top plus stack j with hat on top$ . If $stack c with rightwards arrow on top$ is a vector such that $stack a with rightwards arrow on top. stack c with rightwards arrow on top equals open vertical bar stack c with rightwards arrow on top close vertical bar comma open vertical bar stack c with rightwards arrow on top minus stack a with rightwards arrow on top close vertical bar$ = $2 square root of 2$ and the angle between $open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses$ and $stack c with rightwards arrow on top$ is 30⁰, then find the value of $open vertical bar open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses cross times stack c with rightwards arrow on top close vertical bar$ .

Let $stack a with rightwards arrow on top equals 2 stack i with hat on top plus stack j with hat on top minus 2 stack k with hat on top$ and $stack b with rightwards arrow on top equals stack i with hat on top plus stack j with hat on top$ . If $stack c with rightwards arrow on top$ is a vector such that $stack a with rightwards arrow on top. stack c with rightwards arrow on top equals open vertical bar stack c with rightwards arrow on top close vertical bar comma open vertical bar stack c with rightwards arrow on top minus stack a with rightwards arrow on top close vertical bar$ = $2 square root of 2$ and the angle between $open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses$ and $stack c with rightwards arrow on top$ is 30⁰, then find the value of $open vertical bar open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses cross times stack c with rightwards arrow on top close vertical bar$ .

The equation of the line passing through the point (1, -2, 3) and parallel to the line x – y + 2z = 5 and 3x + y + z = 6 is

The equation of the line passing through the point (1, -2, 3) and parallel to the line x – y + 2z = 5 and 3x + y + z = 6 is

parallel

If (1 + x + x²)ⁿ = a₀ + a₁x + a₂x² + ………+a_2nx²ⁿ, then the value of the determinant $open vertical bar table row cell a subscript n minus 3 end subscript end cell cell a subscript n minus 1 end subscript end cell cell a subscript n plus 1 end subscript end cell row cell a subscript n minus 6 end subscript end cell cell a subscript n minus 3 end subscript end cell cell a subscript n plus 3 end subscript end cell row cell a subscript n minus 14 end subscript end cell cell a subscript n minus 7 end subscript end cell cell a subscript n plus 7 end subscript end cell end table close vertical bar$ is always

If (1 + x + x²)ⁿ = a₀ + a₁x + a₂x² + ………+a_2nx²ⁿ, then the value of the determinant $open vertical bar table row cell a subscript n minus 3 end subscript end cell cell a subscript n minus 1 end subscript end cell cell a subscript n plus 1 end subscript end cell row cell a subscript n minus 6 end subscript end cell cell a subscript n minus 3 end subscript end cell cell a subscript n plus 3 end subscript end cell row cell a subscript n minus 14 end subscript end cell cell a subscript n minus 7 end subscript end cell cell a subscript n plus 7 end subscript end cell end table close vertical bar$ is always

India play two matches each with West Indies and Australia .In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

India play two matches each with West Indies and Australia .In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

If the eccentricities of the hyperbolas $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ and $fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction minus fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction equals 1$ be e and $e subscript 1 end subscript$ , then $fraction numerator 1 over denominator e to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator e subscript 1 end subscript superscript 2 end superscript end fraction equals$

If the eccentricities of the hyperbolas $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ and $fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction minus fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction equals 1$ be e and $e subscript 1 end subscript$ , then $fraction numerator 1 over denominator e to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator e subscript 1 end subscript superscript 2 end superscript end fraction equals$

parallel

The equation of the normal at the point (2, 3) on the ellipse $9 x to the power of 2 end exponent plus 16 y to the power of 2 end exponent equals 180$ , is

The equation of the normal at the point (2, 3) on the ellipse $9 x to the power of 2 end exponent plus 16 y to the power of 2 end exponent equals 180$ , is

The locus of the point of intersection of mutually perpendicular tangent to the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ , is

The locus of the point of intersection of mutually perpendicular tangent to the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ , is

The eccentricity of the curve represented by the equation $x to the power of 2 end exponent plus 2 y to the power of 2 end exponent minus 2 x plus 3 y plus 2 equals 0$ is

The eccentricity of the curve represented by the equation $x to the power of 2 end exponent plus 2 y to the power of 2 end exponent minus 2 x plus 3 y plus 2 equals 0$ is

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.