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Maths-

General

Easy

Question

If $theta$ is the angle between the curves $x y equals 2$ and $x to the power of 2 end exponent plus 4 y equals 0$ , then $tan invisible function application theta$ is equal to

1
-1
2
3

The correct answer is: 3

The point of intersection of given curves are (2, -1)
On differentiating the given curves respectively

$x fraction numerator d y over denominator d x end fraction plus y equals 0 blank rightwards double arrow blank fraction numerator d y over denominator d x end fraction equals negative fraction numerator y over denominator x end fraction$

$rightwards double arrow blank m subscript 1 end subscript equals open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis 2 comma blank minus 1 right parenthesis end subscript equals fraction numerator 1 over denominator 2 end fraction$

And $2 x plus 4 fraction numerator d y over denominator d x end fraction equals 0$

$rightwards double arrow blank m subscript 2 end subscript equals open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis 2 comma blank minus 1 right parenthesis end subscript equals negative 1$

$because blank tan invisible function application theta equals open vertical bar fraction numerator fraction numerator 1 over denominator 2 end fraction plus 1 over denominator 1 minus fraction numerator 1 over denominator 2 end fraction end fraction close vertical bar equals open vertical bar fraction numerator fraction numerator 3 over denominator 2 end fraction over denominator fraction numerator 1 over denominator 2 end fraction end fraction close vertical bar equals 3$

Related Questions to study

Vector sum of two forces of 10 N and 6 N cannot be

Vector sum of two forces of 10 N and 6 N cannot be

For the resultant of two vectors to be maximum, what must be angle between them

For the resultant of two vectors to be maximum, what must be angle between them

The vector sum of the forces of 10 N and 6 N can be

The vector sum of the forces of 10 N and 6 N can be

parallel

$text Given: end text straight A with rightwards arrow on top equals 2 straight i with not stretchy hat on top plus 3 straight j with not stretchy hat on top text and end text straight B with rightwards arrow on top equals 5 straight i with not stretchy hat on top minus 6 straight j with not stretchy hat on top. text The magnitude of end text straight A with rightwards arrow on top plus straight B with rightwards arrow on top text is end text$

$text Given: end text straight A with rightwards arrow on top equals 2 straight i with not stretchy hat on top plus 3 straight j with not stretchy hat on top text and end text straight B with rightwards arrow on top equals 5 straight i with not stretchy hat on top minus 6 straight j with not stretchy hat on top. text The magnitude of end text straight A with rightwards arrow on top plus straight B with rightwards arrow on top text is end text$

The sum, difference and cross product of two vectors $straight A with rightwards arrow on top text and end text straight B with rightwards arrow on top$ are mutually perpendicular if

The sum, difference and cross product of two vectors $straight A with rightwards arrow on top text and end text straight B with rightwards arrow on top$ are mutually perpendicular if

What is the unit vector along $straight i with not stretchy hat on top plus straight j with not stretchy hat on top$ ?

What is the unit vector along $straight i with not stretchy hat on top plus straight j with not stretchy hat on top$ ?

parallel

In [0, 1] Lagranges Mean value theorem is NOT applicable to

In [0, 1] Lagranges Mean value theorem is NOT applicable to

The equation of the normal to the curve $y equals e to the power of negative 2 vertical line x vertical line end exponent$ at the point where the curve cuts the line $x equals 1 divided by 2$ , is

The equation of the normal to the curve $y equals e to the power of negative 2 vertical line x vertical line end exponent$ at the point where the curve cuts the line $x equals 1 divided by 2$ , is

The point in the interval $left square bracket 0 comma blank 2 pi right square bracket$ , where $f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x$ has maximum slope is

The point in the interval $left square bracket 0 comma blank 2 pi right square bracket$ , where $f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x$ has maximum slope is

parallel

The slope of the tangent to the curve $x equals 3 t to the power of 2 end exponent plus 1 comma blank y equals t to the power of 3 end exponent minus 1$ at $x equals 1$ is

The slope of the tangent to the curve $x equals 3 t to the power of 2 end exponent plus 1 comma blank y equals t to the power of 3 end exponent minus 1$ at $x equals 1$ is

The function $f open parentheses x close parentheses equals not stretchy integral from negative 1 to x of t open parentheses e to the power of t end exponent minus 1 close parentheses open parentheses t minus 1 close parentheses open parentheses t minus 2 close parentheses to the power of 3 end exponent open parentheses t minus 5 close parentheses to the power of 5 end exponent d t$ has local minimum at $x equals$

The function $f open parentheses x close parentheses equals not stretchy integral from negative 1 to x of t open parentheses e to the power of t end exponent minus 1 close parentheses open parentheses t minus 1 close parentheses open parentheses t minus 2 close parentheses to the power of 3 end exponent open parentheses t minus 5 close parentheses to the power of 5 end exponent d t$ has local minimum at $x equals$

The edge of a cube is equal to the radius of a sphere. If the edge and the radius increase at the same rate, then the ratio of the increases in surface areas of the cube and sphere is

The edge of a cube is equal to the radius of a sphere. If the edge and the radius increase at the same rate, then the ratio of the increases in surface areas of the cube and sphere is

parallel

The minimum value of $x to the power of 2 end exponent plus fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction i s blank a t$

The minimum value of $x to the power of 2 end exponent plus fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction i s blank a t$

The equation of motion of a particle moving along a straight line is s=2 $t to the power of 3 end exponent minus 9 t to the power of 2 end exponent plus 12 t comma$ where the units of s and t are centimeter and second. The acceleration of the particle will be zero after

The equation of motion of a particle moving along a straight line is s=2 $t to the power of 3 end exponent minus 9 t to the power of 2 end exponent plus 12 t comma$ where the units of s and t are centimeter and second. The acceleration of the particle will be zero after

A minimum value of $not stretchy integral subscript 0 end subscript superscript x end superscript t e to the power of t to the power of 2 end exponent end exponent d t$ is

A minimum value of $not stretchy integral subscript 0 end subscript superscript x end superscript t e to the power of t to the power of 2 end exponent end exponent d t$ is

parallel

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