Find an equation for the parabola that has its vertex at the origin and satisfies the given condition. Focus F(−5, 0)

Answer 1

The vertex of a parabola is usually notated by (h,k). Since it is at the origin, the vertex is (0,0), so h=0 and k=0.

For parabolas, you can either have it go "up and down" (where the shape either looks like a U or a mountain), or have it go "sideways" (where the shape of the graph looks like ( or ).)

If the parabola goes up and down, the equation is y-k=a(x-h)², and the focus is the point (h,k+1/4a).

If the parabola goes sideways, the equation is a(y-k)^2=(x-h), and the focus is (h+1/4a,k).

To find the equation of the parabola, we just need to solve for a using the focus formula, the values we have for our focus, our values for h and k, and knowing that cannot be equal to 0. Based on the formulas we have, it cannot go up and down. Our focus is (-5,0) and our center is (0,0), so plugging those values into the focus formula we get an invalid statement -5=0

Plugging everything into the sideways formula, we get -5=0+1/4a. Solving the equation, we get a=1/-20. So the equation would be 1/-20(y+5)^2=x