Question

What is the focus of the parabola given by the equation
(y − 3)2 = 8(x − 5)?

Answer 1

This is that standard form of a parabola, which is \[(y-k)^{2}=4px\]where the p is used to find the focal point. This parabola sits at (5, 3), and the coefficient in front of the x term is 8. So we use the formula 4p=8 to find the focal point. Divide by 4 and get p = 2. So your focal point, if the parabola was sitting at the origin would be (2, 0). But it is at (5, 3), so we need to move the focal point that number of coordinates from (2, 0) to (2 + 5, 0 + 3). The focal point is located at (7, 3). Here's what it looks like

Answer 2

Do you have any idea of how to find the focal point of a parabola? If not I can try to explain it to you!