Question

The slope of the tangent at $(1,6)$ on the curve $2x^2+3y^2=5$ is

• A. $-9$
• B. $\frac{-1}{9}$
• C. $\frac{1}{9}$
• D. $9$

Answer 1

The correct option is B $\frac{-1}{9}$

The equation of tangent at $(x_1,y_1)$ to the ellipse $2x^2+3y^2=5$ is $2x{x}_1+3y{y}_1=5$......(1).

Here $x_1=1$ and $y_1=6$.

Putting these values of $x_1$ and $y_1$ in equation (1) we get,

$2x+18y=5$.

or, $y=-\frac{1}{9}x+\frac{5}{18}$

Slope of the tangent is $-\frac{1}{9}$.