Question

If the tangent at any point on the curve \(x^4 + y^4 = a^4^\) cuts off intercepts p and q on the coordinate axes, the value of $p^{-\frac{4}{3}}+q-\frac{4}{3}$ is

• A. $a^{-\frac{4}{3}}$
• B. $a^{-\frac{1}{2}}$
• C. $a^{\frac{1}{2}}$
• D. $Noneofthese$

Answer 1

The correct option is C $a^{\frac{1}{2}}$

$x=\frac{siny}{sin(a+y)}$ . . . .(i)
$\Rightarrow \frac{dx}{dy}=\frac{sin\left(a\right)}{si{n}^2(a+y)}\therefore \frac{dy}{dx}=\frac{si{n}^2(a+y)}{sin\left(a\right)}=\frac{A}{1+x^2-2xcosa}$
Put x = 0, y = 0,
then~A = sin a