Question

The equation of the parabola whose vertex and focus are on the positive side of the x-axis at distances $a$ and $b$ respectively from the origin is

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

Answer 1

The correct option is A $y^2=4(b-a)(x-a)$

Given vertex of the parabola is $x=a$
and focus at $(b,0)$
So the latus rectum of the parabola is $=4(b-a)$
Also tangent on the vertex will be $x=a$
Thus equation of required parabola is, $y^2=4(b-a)(x-a)$
Note: There are other possibility also depending on the values of 'a' and 'b'.