Question

The product of the slopes of the tangents to the ellipse $2x^2+3y^2=6$ drawn from the point (1, 2) is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\frac{x^2}{3}+\frac{y^2}{2}=1$
$y=mx\pm \sqrt{a^2{m}^2+b^2}$ is the equation of the tangent.
It passes through (1,2)
$2=m\pm \sqrt{3m^2+2}\sqrt{3m^2+2}=m-23m^2+2=m^2-4m+42m^2-4m-2=0m^2-2m-1=0$
Product of slopes = - 1