Let P be the parabola whose focus is (-2,1) and directrix is 2x+y+2=0.

Question

Let $P$ be the parabola whose focus is $(-2,1)$ and directrix is $2x+y+2=0$. Then the sum of the ordinates of the points on $P$ whose abscissa is $-2$, is:

Accepted Answer

At $x=-2$, distance to directrix $=$ distance to focus:

$$\frac{|2(-2)+y+2|}{\sqrt5}=\sqrt{(-2+2)^2+(y-1)^2}=|y-1|.$$

$$(y-2)^2=5(y-1)^2 \;\Rightarrow\; 4y^2-6y+1=0.$$

Sum of ordinates $=\dfrac64=\dfrac32$.

Solutions · 1