Question

What is the focus of the parabola given by the equation (y − 3)^2 = 8(x − 5)? A. (-7, 3) B. (-5, 3) C. (5, 3) D. (7, 3) E. (3, -7)

Answer 1

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let's notice, the squared variable is the "y", and therefore is a horizontal parabola, with a vertex as you see at 5,3.

the coefficient of the y² is positive, meaning it opens to right-hand-side.

the "p" distance is 2 units, since it's opening to the right, is positive 2.

so from the vertex at 5,3 we move to the right 2 units, to land at (7, 3).