CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Representation of Point on the Plane

If the length...

Question

If the length of subnormal at point $P (a, a)$ on the curve $y^{2} = \frac{x^{3}}{2 a - x}$
is equal to $k$ times the length of subtangent, then the value of $k^{2}$ is equal to

Open in App

Solution

$y^{2} = \frac{x^{3}}{2 a - x} \Rightarrow y^{2} (2 a - x) = x^{3}$
dif w.r.t $x$
$\Rightarrow (2 a - x) \cdot 2 y y^{'} - y^{2} = 3 x^{2}$

at $P (a, a), y^{'} = 2 = m$

$S T = ∣ ∣ \frac{y_{1}}{m} ∣ ∣ = \frac{| a |}{2}$

$S N = | y_{1} m | = 2 | a |$

$\Rightarrow S N = 4 S T \Rightarrow k = 4 \Rightarrow k^{2} = 16$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If at any point on a curve the subtangent and subnormal are equal then the length of the tangent equal to :

Q. If at any point

(x_{1}, y_{1})

on a curve the subtangent and subnormal are equal then the length of tangent is equal to

Q. If length of subnormal to the curve

y = x^{2} - 3 x + 2

x = 3

is equal to the length of subtangent to the curve

y = x^{2} + 2 x + a,

then the number of non-negative integral value(s) of

a

Q. At any point of a curve (subtangent)

\times

(subnormal) is equal to the square of the -

Q. I. lf the subnormal to the curve

x \times y^{n} = a^{n + 1}

is constant, then the value of

n

- 2

.
II. The length of the subtangent, ordinate of a point, length of the subnormal on a point other than the origin to the curve

y^{2} = 4 a x

G . P

.
Which of the above statements is correct?

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Representation of Point on the Plane

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon