Question: The tangent to the curve 2y3 = ax2 + x3 drawn at the point (a, a) ...

Question

The tangent to the curve 2y³ = ax² + x³ drawn at the point

(a, a) cuts l, m intercepts on coordinate axes where

l² + m² = 16. Then |a| is equal to –

Answer 1

$\left( \frac{dy}{dx} \right)_{(a,a)}$ = $\frac{2ax + 3x^{2}}{6y^{2}}$ = $\frac{5a^{2}}{6a^{2}}$ = $\frac{5}{6}$

equation of tangent ® y – a = $\frac{5}{6}$ (x – a)

Ž $\frac{x}{\left( –\frac{a}{5} \right)}$ + $\frac{y}{\left( \frac{a}{6} \right)}$ = 1

given $\left( –\frac{a}{5} \right)^{2}$ + $\left( \frac{a}{6} \right)^{2}$ = 1 Ž a² = (25) (36)

|a| = 30

Question: The tangent to the curve 2y<sup>3</sup> = ax<sup>2</sup> + x<sup>3</sup> drawn at the point (a, a) ...