Question

If the tangent to the curve 2y³ = ax² + x³ at the point (a, a) cuts off intercepts a and b on the coordinate axes, where

a² + b² = 61 then the value of | a | is –

• A. 16
• B. 28
• C. 30
• D. 31

Answer 1

Answer: (C)

30

Answer 2

The slope of the tangent is

$\frac{dy}{dx}$ =$\frac{2ax + 3x^{2}}{6y^{2}}$

and the value of this slope at (a, a) is 5/6.

Therefore, the equation

y – a = $\frac{5}{6}$ (x – a)

Ž $\frac{x}{- a/5}$ + $\frac{y}{a/6}$ = 1,

represents the tangent. Thus the x-intercept a is –a/5, and the y-intercept b is a/6. From a² + b² = 61, we now get $\frac{a^{2}}{25} + \frac{a^{2}}{36}$ = 61

Ž a² = 25 × 36 Ž a = ± 30.