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

Question

Aicharya · Accepted Answer

Equation of parabola
$(x+2)^2+(y-1)^2=\left(\frac{2 x+y+2}{\sqrt{5}}\right)^2$

$5\left[(x+2)^2+(y-1)^2\right]=(2 x+y+2)^2$
Put $x=-2,5(y-1)^2=(y-2)^2$
$\begin{aligned}
& 5\left(y^2-2 y+1\right)=y^2-4 y+4 \\ & \Rightarrow 4 y^2-6 y+1=0 \Rightarrow y_1+y_2=\frac{3}{2}
\end{aligned}$ .

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

Solution