Focal distance on a parabola

Question

If focal distance of a point on the parabola $y = x^2 - 4$ is $25/4$ . And the points are of form $(\pm \sqrt{a}, b$ then how can we find $a , b$ or sum of these . I think the focus of parabola would be $(0, -15/4)$ and we get $a-b=4$ by putting the coordinates in parabola eq. . And if use distance formula then we get $a + b^2 + 225/4 + 15b/2 = 625/16$ . But in this we have one equation of quadratic and one of linear

Answer 1

There is a mistake in your equation: the $\frac{225}{4}$ should be $\frac{225}{16}$.

Hint:

You can do substitution $a=b+4$. Plug this into the second equation will give you a quadratic equation for $b$.