Question
Question: A parabola is drawn with its focus (3, 4) and vertex at the focus of the parabola y<sup>2</sup> – 12...
A parabola is drawn with its focus (3, 4) and vertex at the focus of the parabola y2 – 12 x – 4y + 4 = 0. The equation of the parabola is –
A
x2 – 6x – 8y + 25 = 0
B
y2 – 8x – 6y + 25 = 0
C
x2 – 6x + 8y – 25 = 0
D
x2 + 6x – 8y – 25 = 0
Answer
x2 – 6x – 8y + 25 = 0
Explanation
Solution
Since, y2 – 12 x – 4y + 4 = 0 ̃ (y – 2)2 = 12 x
̃ Vertex is (0, 2) focus is (3, 2)
\ Vertex of the required parabola is (3, 2) and focus is (3, 4). The axis of symmetry is x = 3 and latus-rectum = 4.2 = 8. Hence, required equation is
(x – 3)2 = 8 (y – 2) \ x2 – 6x – 8y + 25 = 0