Question

The equation of the parabola whose vertex and focus lie on the $x-$axis at distances $a$ and $a_1$ $(0<a<a_1)$ 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. $\text{none of these}$

Answer 1

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

The coordinates of the focus and vertex of the required parabola are $S(a_1,0)$ and $A(a,0)$, respectively.
Therefore, the distance between the vertex and focus is $AS=a_1-a$
and so, the the length of the latus rectum $=4(a_1-a)$.
Thus, the equation of the parabola is
$y^2=4(a_1-a)(x-a)$.