The axis of a parabola is the line $y=x$ and its vertex and focus are in the first quadrant at distances $\sqrt{2}$ and $2 \sqrt{2}$ units from the origin, respectively. If the point $(1, \mathrm{k})$ lies on the parabola, then a possible value of $k$ is :-

Question

Aicharya · Accepted Answer

Directrix $x+y=0$
$\begin{aligned}
& \mathrm{PS}=\mathrm{PM} \\ & \sqrt{(1-2)^2+(\mathrm{K}-2)^2}=\frac{(1+\mathrm{K})}{\sqrt{2}} \\ & 2 \mathrm{~K}^2+8-8 \mathrm{~K}+2=\mathrm{K}^2+1+2 \mathrm{~K} \\ & \mathrm{~K}^2-10 \mathrm{~K}+9=0 \\ & \mathrm{~K}=9 \\ & \text { option (2) }
\end{aligned}$ /

The axis of a parabola is the line $y=x$ and its vertex and focus are in the first quadrant at distances…

Solution