JEE Main 2017 — Application Of Derivatives Question with Solution

As,    $$\frac{dy}{dx}$$ = $$-$$ $$\left[\frac{\frac{\delta f}{\delta x}}{\frac{\delta f}{\delta y}}\right]$$

$$\frac{\delta f}{\delta x}$$ = y² $$\times$$2x $$-$$ 2

$$\frac{\delta f}{\delta y}$$ = x² $$\times$$ 2y + 4

$$\therefore$$ $$\frac{dy}{dx}$$ = $$-$$ $$\left(\frac{2x{y}^2-2}{2x^{2}y+4}\right)$$

$${\left[\frac{dy}{dx}\right]}_{(2,-2)}$$ = $$-$$ $$\left(\frac{2\times 2\times 4-2}{2\times 4\times (-2)+4}\right)$$ = $$-$$ $$\left(\frac{14}{-12}\right)$$ = $$\frac{7}{6}$$

$$\therefore$$ Slope of tangent to the curve = $$\frac{7}{6}$$

Equation of tangent passes through (2, $$-$$ 2) is

y + 2 = $$\frac{7}{6}$$ (x $$-$$ 2)

$$\Rightarrow$$ 7x $$-$$ 6y = 26 . . . . .(1)

Now put each option in equation (1) and see which one does not satisfy the equation.

By verifying each points you can see ($$-$$ 2, $$-$$ 7) does not satisfy the equation.