Question

The equation of the parabola whose vertex is (-1, -2), axis is vertical and which passes through the point (3, 6), is

• A. \(x^2 + 2x - 2y - 3 = 0\)
• B. \(2x^2 = 3y\)
• C. \(x^2 - 2x + 2y - 3 = 0\)
• D. \(x^2 - 2x - 2y - 3 = 0\)

Hint:

For vertical axis parabola: \((x - h)^2 = 4a(y - k)\), opens upward if \(a>0\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Vertical axis parabola: \((x - h)^2 = 4a(y - k)\) with vertex \((h, k)\).
Step 2: Detailed Explanation:
Equation: \((x + 1)^2 = 4a(y + 2)\)
Passes through (3,6): \((4)^2 = 4a(8) \rightarrow 16 = 32a \rightarrow a = 1/2\)
\((x + 1)^2 = 2(y + 2) \rightarrow x^2 + 2x + 1 = 2y + 4 \rightarrow x^2 + 2x - 2y - 3 = 0\)
Step 3: Final Answer:
\(x^2 + 2x - 2y - 3 = 0\).