Question

Focus of the parabola \(y^2 - 8x - 32 = 0\) is:

• A. (2, 0)
• B. (-2, 0)
• C. (0, 2)
• D. (4, 0)

Hint:

Always rewrite the parabola equation in standard form to quickly identify the vertex and focal length \(a\).

Answer 1

The Correct Option is B

We have:
\[ y^2 - 8x - 32 = 0 \] Rewrite:
\[ y^2 = 8x + 32 \] Factor out 8 from the right-hand side:
\[ y^2 = 8(x + 4) \] This is of the form \(y^2 = 4a(x - h)\) with vertex at \((-4, 0)\) and \(4a = 8 \Rightarrow a = 2\).
Since the parabola opens to the right, the focus is at \((h + a, k) = (-4 + 2, 0) = (-2, 0)\).