Question

Slope of tangent to $x^2=4y$ from (-1, -1) can be

• A. $\frac{-1\pm \sqrt{5}}{2}$
• B. $\frac{-3-\sqrt{5}}{2}$
• C. $\frac{1-\sqrt{5}}{2}$
• D. $\frac{1+\sqrt{5}}{2}$

Answer 1

The correct option is A $\frac{-1\pm \sqrt{5}}{2}$

$y^1=\frac{x}{2}=m$
$\Rightarrow x=2m\Rightarrow y=m^2$
So equation of tangent is $y-m^2=m(x-2m)$ which passes through (-1, -1)
$\Rightarrow -1-m^2=m(-1-2m)$
$\Rightarrow m^2+m-1=0\Rightarrow m=\frac{-1\pm \sqrt{5}}{2}$