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  4. The equation of the parabola with vertex at (-1,1) and focus (2,1) is :

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Q. The equation of the parabola with vertex at $(-1,1)$ and focus $(2,1)$ is :

KCETKCET 2006Conic Sections

Solution:

By the condition of parabola
$PM^2 = PS^2$
$\Rightarrow \, (x + 4)^2 = (x-2)^2 +(y - 1)^2$
image
$\Rightarrow \, x^2 + 8x - 16 =x^2 - 4x + 4 + y^2 - 2y + 1$
$\Rightarrow \, y^2 - 2y - 12x - 11 = 0 $