Question

The sum of the slopes of the tangents to the parabola $y^2=8x$ from the point $(-2,3),$ is

• A. $-2$
• B. $-3$
• C. $\frac{-3}{2}$
• D. $2$

Answer 1

The correct option is C $\frac{-3}{2}$

Equation of tangent to parabola $y^2=8x$ is given by,
$y=mx+\frac{a}{m}\Rightarrow y=mx+\frac{2}{m}$

As it passes through $(-2,3)$
$\Rightarrow 3=-2m+\frac{2}{m}\Rightarrow 3m=-2m^2+2\Rightarrow 2m^2+3m-2=0$

$\therefore$ Sum of slopes $=-\frac{3}{2}$