Question

The normal to the curve $2x^2+y^2=12$ at the point $(2,2)$ cuts the curve again at

• A. $(-\frac{22}{9},-\frac{2}{9})$
• B. $\left(\frac{22}{9},\frac{2}{9}\right)$
• C. $(-2,-2)$
• D. none of these

Answer 1

The correct option is A $(-\frac{22}{9},-\frac{2}{9})$

Given equation of curve is

$2x^2+y^2=12$

$\frac{dy}{dx}=-\frac{2x}{y}$

Slope of tangent at (2,2) is -2.

Slope of normal at (2,2) is $\frac{1}{2}$

Equation of normal at (2,2) is

$y-2=\frac{1}{2}(x-2)$

$\Rightarrow 2y-x=2$

Here , we can solve by checking options.

So ,option A satisfies above equation.

Hence $(-\frac{22}{9},-\frac{2}{9})$ is the required point.