Question

The equation of the parabola whose vertex and focus lie on the axis of $x$ at distances $a$ and $a_1$ from the origin respectively is:

• A. $y^2=4(a_1-a)x$
• B. $y^2=4(a_1-a)(x-a)$
• C. $y^2=4(a_1-a)(x-a_1)$
• D. none of these

Answer 1

The correct option is B $y^2=4(a_1-a)(x-a)$

Vertex A is $(a,0)$
Focus S is $(a_1,0)$
Distance between vertex and focus $AS=a_1-a=A\left(say\right)$
So, the equation of parabola with vertex at $(a,0)$ is
$(y-0{)}^2=4A(x-a)$
$\Rightarrow (y-0{)}^2=4(a_1-a\left)\right(x-a)$
$\Rightarrow y^2=4(a_1-a)(x-a)$