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Q.
Find the equation of the parabola with focus $(2, 0)$ and directrix $x = - 2$.
Conic Sections
Solution:
Since the focus $(2, 0)$ lies on the $x$-axis, the $x$-axis itself is the axis of the parabola. Hence the equation of the parabola is of the form $y^{2} = 4ax$ or $y^{2 }= -4ax$. Since the directrix is $x = -2$ and the focus is $(2, 0)$, the parabola is to be of the form $y^{2} = 4ax$ with $a = 2$. Hence the required equation is $y^{2} = 4(2)x = 8x$.