Question

If the vertex of the parabola is the of the point(–3, 0) and the directrix is the line x + 5 = 0, then its equation is
(a) y² = 8 (x + 3)
(b) x² = 8 (y + 3)
(c) y² = –8 (x + 3)
(d) y² = 8 (x + 5)

Answer 1

Given that vertex is (−3, 0) and directrix is x + 5 = 0

Let P(x, y) be any point on parabola,
Let S determine focus i.e. S(−1, 0)
Since SP = PM
$$\begin{gathered} \mathrm{i}.\mathrm{e}.\sqrt{{\left(x+1\right)}^2+y^2}=\frac{\left|x+5\right|}{\sqrt{1}} \\ \mathrm{i}.\mathrm{e}.\sqrt{{\left(x+1\right)}^2+y^2}=\left|x+5\right| \end{gathered}$$

Now, squaring both sides,

$$\begin{gathered} \mathrm{i}.\mathrm{e}.{\left(x+1\right)}^2+y^2={\left|x+5\right|}^2 \\ \mathrm{i}.\mathrm{e}.x^2+2x+1+y^2=x^2+10x+25 \\ \mathrm{i}.\mathrm{e}.y^2=8x+24 \\ \mathrm{i}.\mathrm{e}.y^2=8\left(x+3\right) \end{gathered}$$

Hence, the correct answer is option A.