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

If $S T$ and $S N$ are the lengths of the subtangent and the subnormal at the point $theta equals fraction numerator pi over denominator 2 end fraction$ on the curve $x equals a open parentheses theta plus sin invisible function application theta close parentheses comma blank y equals a open parentheses 1 minus cos invisible function application theta close parentheses comma blank a not equal to 1$ , then

$S T = S N$
$S T = 2 S N$
$S T^{2} = a S N^{3}$
$S T^{3} = a S N$

The correct answer is: $S T equals S N$

Given,
$x equals a left parenthesis theta plus sin invisible function application theta right parenthesis$ and $y equals a left parenthesis 1 minus cos invisible function application theta right parenthesis$

$rightwards double arrow blank fraction numerator d x over denominator d theta end fraction equals a left parenthesis 1 plus cos invisible function application theta right parenthesis$ and $fraction numerator d y over denominator d theta end fraction equals a sin invisible function application theta$

$therefore blank fraction numerator d y over denominator d x end fraction equals fraction numerator a sin invisible function application theta over denominator a left parenthesis 1 plus cos invisible function application theta right parenthesis end fraction equals tan invisible function application fraction numerator theta over denominator 2 end fraction$

Now, length of subtangent $equals open vertical bar fraction numerator y over denominator d y divided by d x end fraction close vertical bar$

$therefore blank S T equals fraction numerator a left parenthesis 1 minus cos invisible function application theta right parenthesis over denominator tan invisible function application left parenthesis theta divided by 2 right parenthesis end fraction equals a sin invisible function application theta$

$rightwards double arrow$ Length of suntangent at $theta equals fraction numerator pi over denominator 2 end fraction$ ,

$S T equals a sin invisible function application fraction numerator pi over denominator 2 end fraction equals a$

And length of subnormal $equals open vertical bar y fraction numerator d y over denominator d x end fraction close vertical bar$

$rightwards double arrow blank S N equals a open parentheses 1 minus cos invisible function application theta close parentheses. tan invisible function application fraction numerator theta over denominator 2 end fraction$

$equals a.2 sin to the power of 2 end exponent invisible function application fraction numerator theta over denominator 2 end fraction tan invisible function application fraction numerator theta over denominator 2 end fraction$

$rightwards double arrow$ Length of subnormal at $theta equals fraction numerator pi over denominator 2 end fraction$ ,

$S N plus a.2.1.2 equals a$

Hence, $S N equals S T$

Related Questions to study

The tangent to the curve $y equals x to the power of 3 end exponent minus 6 x to the power of 2 end exponent plus 9 x plus 4 comma blank 0 less or equal than x less or equal than 5$ has maximum slope at $x$ which is equal to

The tangent to the curve $y equals x to the power of 3 end exponent minus 6 x to the power of 2 end exponent plus 9 x plus 4 comma blank 0 less or equal than x less or equal than 5$ has maximum slope at $x$ which is equal to

The line $left parenthesis x divided by a right parenthesis plus left parenthesis y divided by b right parenthesis equals 2$ , touches the curve $fraction numerator x to the power of n end exponent over denominator a to the power of n end exponent end fraction plus fraction numerator y to the power of n end exponent over denominator b to the power of n end exponent end fraction equals 2$ , at

The line $left parenthesis x divided by a right parenthesis plus left parenthesis y divided by b right parenthesis equals 2$ , touches the curve $fraction numerator x to the power of n end exponent over denominator a to the power of n end exponent end fraction plus fraction numerator y to the power of n end exponent over denominator b to the power of n end exponent end fraction equals 2$ , at

The length of the subtangent to the curve $x to the power of 2 end exponent plus x y plus y to the power of 2 end exponent equals 7$ at $left parenthesis 1 comma blank minus 3 right parenthesis$ is

The length of the subtangent to the curve $x to the power of 2 end exponent plus x y plus y to the power of 2 end exponent equals 7$ at $left parenthesis 1 comma blank minus 3 right parenthesis$ is

parallel

The equation of the tangent to the curve $x equals 2 cos to the power of 3 end exponent invisible function application theta$ and $y equals 3 sin to the power of 3 end exponent invisible function application theta$ at the point, $theta equals pi divided by 4$ is

The equation of the tangent to the curve $x equals 2 cos to the power of 3 end exponent invisible function application theta$ and $y equals 3 sin to the power of 3 end exponent invisible function application theta$ at the point, $theta equals pi divided by 4$ is

If $f open parentheses x close parentheses equals fraction numerator 1 over denominator x plus 1 end fraction minus log invisible function application left parenthesis 1 plus x right parenthesis comma blank x greater than 0$ , then $f$ is

If $f open parentheses x close parentheses equals fraction numerator 1 over denominator x plus 1 end fraction minus log invisible function application left parenthesis 1 plus x right parenthesis comma blank x greater than 0$ , then $f$ is

Let $P left parenthesis 2 comma blank 2 right parenthesis$ and $Q left parenthesis 1 divided by 2 comma blank minus 1 right parenthesis$ be two points on the parabola $y to the power of 2 end exponent equals 2 x$ . The coordinates of the point $R$ on the parabola $y to the power of 2 end exponent equals 2 x$ , where the tangent to the curve is parallel to the chord $P Q$ , are

Let $P left parenthesis 2 comma blank 2 right parenthesis$ and $Q left parenthesis 1 divided by 2 comma blank minus 1 right parenthesis$ be two points on the parabola $y to the power of 2 end exponent equals 2 x$ . The coordinates of the point $R$ on the parabola $y to the power of 2 end exponent equals 2 x$ , where the tangent to the curve is parallel to the chord $P Q$ , are

parallel

The sum and difference of two perpendicular vectors of equal length are

The sum and difference of two perpendicular vectors of equal length are

If a current of $5 blank A$ in a coil of self inductance $2 blank m H$ is cut off in time $0.1 blank s$ , the induced $e m f$ in the coil is

If a current of $5 blank A$ in a coil of self inductance $2 blank m H$ is cut off in time $0.1 blank s$ , the induced $e m f$ in the coil is

Physics-General

A coil having an area $2 m to the power of 2 end exponent$ is placed in a magnetic field which changes from $1 W b divided by m to the power of 2 end exponent$ to $4 W b divided by m to the power of 2 end exponent$ in an interval of $2 blank s e c o n d$ . The e.m.f. induced in the coil will be

A coil having an area $2 m to the power of 2 end exponent$ is placed in a magnetic field which changes from $1 W b divided by m to the power of 2 end exponent$ to $4 W b divided by m to the power of 2 end exponent$ in an interval of $2 blank s e c o n d$ . The e.m.f. induced in the coil will be

Physics-General

parallel

The wing span of an aeroplaneis $20 blank m e t r e$ . It is flying in a field, where the vertical component of magnetic field of earth is $5 cross times 10 to the power of negative 5 end exponent t e s l a$ , with velocity $360 blank k m divided by h$ . The potential difference produced between the blades will be

The wing span of an aeroplaneis $20 blank m e t r e$ . It is flying in a field, where the vertical component of magnetic field of earth is $5 cross times 10 to the power of negative 5 end exponent t e s l a$ , with velocity $360 blank k m divided by h$ . The potential difference produced between the blades will be

Physics-General

The index of the highest power of 3 that divides 50! is -

The index of the highest power of 3 that divides 50! is -

A square coil of $10 to the power of negative 2 end exponent m to the power of 2 end exponent$ area is placed perpendicular to a uniform magnetic field of intensity $10 to the power of 3 end exponent W b divided by m to the power of 2 end exponent$ . The magnetic flux through the coil is

A square coil of $10 to the power of negative 2 end exponent m to the power of 2 end exponent$ area is placed perpendicular to a uniform magnetic field of intensity $10 to the power of 3 end exponent W b divided by m to the power of 2 end exponent$ . The magnetic flux through the coil is

Physics-General

parallel

The number of proper divisors of 2p. 6q. 15r is-

The number of proper divisors of 2p. 6q. 15r is-

In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon is -

In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon is -

The number of triangles whose vertices are at the vertices of an octagon but none of sides happen to come from the sides of the octagon is-

The number of triangles whose vertices are at the vertices of an octagon but none of sides happen to come from the sides of the octagon 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.