Question
Question: The focus is at (2, 3) and the foot of the perpendicular from the focus on the directrix is (4, 5). ...
The focus is at (2, 3) and the foot of the perpendicular from the focus on the directrix is (4, 5). The equation of the parabola is
A
(x - 2)2 + (y - 3)2=(x + y - 9)2
B
(x-2)2 + (y-3)2 = (x + y + 9)2
C
(x - 2)2 + (y - 3)2=(x - y - 9)2
D
2[(x - 2)2 + (y - 3)2] = (x + y - 9)2
Answer
2(x−2)<sup>2</sup>+(y−3)<sup>2</sup> = (x + y - 9)2
Explanation
Solution
Focus S = (2, 3), the foot of the perpendicular from focus to the directrix Z = (4, 5).
Slope of SZ = 1.
∴ Slope of directrix = -1
Since directrix passes through Z, the equation of directrix is y – s = -1 (x-d).
∴The equation parabola is SP2 = PM2 (If P (x, y) be any point on the parabola)
⇒ 2[(x-2)2 + (y-3)2] = (x+y – 9)2