Question

One focus and the corresponding directrix of an ellipse are (1, 2) and x - y = 5. Its eccentricity is ½. Then centre is

• A. (3, 0)
• B. (0, 3)
• C. (3, 3)
• D. (0, 0)

Answer 1

Answer: (B)

(0, 3)

Answer 2

Let Z (h, k) be the foot of the perpendicular from S(1, 20 to the directrix x – y – 5 = 0.

Then $\frac{h - 1}{1} = \frac{k - 2}{- 1} = \frac{- (1 - 2 - 5)}{1 + 1}$ ⇒ (h, k) = (4, -1)

The centre ‘c’ divides SZ in the ratio –e² : 1 (given e = ½)

∴ c = (0, 3)