Find the equation of the parabola with focus

Question:

Find the equation of the parabola with focus $F(4,0)$ and directrix $x=-4$.

Solution:

Given equation of directrix : $x=-4$

• x + 4 = 0

Above equation is of the form, $x+a=0$

Focus of the parabola $F(4,0)$ is of the form $F(a, 0)$

Therefore, $\mathrm{a}=4$

For directrix with equation $\mathrm{x}+\mathrm{a}=0$ and focus $(\mathrm{a}, 0)$, equation of the parabola is,

$y^{2}=4 a x$

$\cdot y^{2}=16 x$

 

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