A parabola is drawn with its focus at (3, 4) and vertex at the focus of the parabola y2 – 12x – 4y + 4 = 0. The equation of the parabola is

Engineering

Mathematics

Standard Parabola

Question

A parabola is drawn with its focus at (3, 4) and vertex at the focus of the parabola y² – 12x – 4y + 4 = 0. The equation of the parabola is

y² – 8x – 6y + 25 = 0

x² – 6x + 8y – 25 = 0

x² + 6x – 8y – 25 = 0

x² – 6x – 8y + 25 = 0

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(y – 2)² = 12x = 4·3x
⇒ Focus : (3, 2)
   New parabola
focus : (3, 4)
vertex : (3, 2)
⇒    (x – 3)² = 4 · 2 (y – 2)
⇒    x² – 6x – 8y + 25 = 0   Ans.

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