Question

The number of tangents to the curve x^3/2 + y^3/2 = a^3/2 where the tangents are equally inclined to the axes, is

• A. 2
• B. 1
• C. 4
• D. None of these

Answer 1

Answer: (B)

1

Answer 2

$\frac{dy}{dx} = \frac{- x^{1/2}}{y^{1/2}}$ Now tangent is equally inclined to axis whose slope is ± 1

\ $\left. \ \frac{dy}{dx} \right|_{\alpha,\beta} = 1$ Ž a^1/2 + b^1/2 = 0 …..(1)

also a^3/2 + b^3/2 = a^3/2 .….(2)

(1) & (2) have no solution

Now $\left. \ \frac{dy}{dx} \right|_{\alpha,\beta} = - 1$ Ž a^1/2 = b^1/2 Ž a = b

\ a^3/2 + b^3/2 = a^3/2 ; Ž a = b = $\frac{a}{2}\frac{2}{3}$

Ž there is only one solution