My question is how can I find the distance from the focus to the vertex of a parabola with the given equation y^2=-10x. Can someone please explain and help me with the answer??

You need to memorize the following: the basic form of the equation for a parabola is:


y-y_o = \frac 1 {4p} (x-x_o)^2



Where (x_o, y_o) is the coordinates of the vertex of the parabola, and p is the distance from the vertex to the focus.

In your problem there's a bit of trick - the x and y coordinats are switched around (so that the parabola will be lying on its side). But the same concept aplies. So reconfigure your equation y^2 = -10x into the form:

(x-x_o) = 1/4p (y - y_o)^2

and you'll get your value for p.