If the length of subnormal at point Pa- a on the curve y2-x32 a-xis equal to k times the length of subtangent- then the value of k2 is equal to

Y^2=x^32 a x⇒ y^2(2 a x)=x^3 dif w.r.t x ⇒(2 a x) · 2 y y^' y^2=3 x^2 at P(a, a) ,y^'=2=m S T=|y_1m|=|a|2 S N=|y_1 m|=2|a| ⇒SN=4 ST⇒ k=4 ⇒ k^2=16 nbsp; ...

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Standard VIII

Mathematics

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

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

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

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

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

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Representation of Point on the Plane

Standard VIII Mathematics

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If the length of subnormal at point P(a,a) on the curve y2=x32a−x is equal to k times the length of subtangent, then the value of k2 is equal to

y2=x32a−x⇒y2(2a−x)=x3 dif w.r.t x ⇒(2a−x)⋅2yy′−y2=3x2 at P(a,a),y′=2=m ST=∣∣y1m∣∣=|a|2 SN=|y1m|=2|a| ⇒SN=4ST⇒k=4⇒k2=16

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