Question

Find the equation of tangents to the ellipse $3x^2+4y^2=12$ which are perpendicular to the line $y+2x=4.$ The equation is given by $y=mx\pm b$, find $m\times b.$

• A. $\frac{1}{2}$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is B $1$

The ellipse is $\frac{x^2}{4}+\frac{y^2}{3}=1$ $\therefore a^2=4,b^2=3$

Slope of the line $y+2x=4$ is $-2.$
Any tangent to the ellipse is $y=mx\pm \sqrt{(a^2{m}^2+b^2)}$
If it is perpendicular to given line then $m=\frac{1}{2}$
$y=\frac{1}{2}x\pm 2$
$\Rightarrow m\times b=1$
Ans: B