Question

The equation of an ellipse whose focus is (–1, 1) and whose directrix is x – y + 3 = 0 and eccentricity is $\frac{1}{2}$ is-

• A. 7x² + 2xy + 7y² + 10x – 10 y + 7 = 0
• B. 7x² – 2xy + 7y² – 10x + 10y + 7 = 0
• C. 7x² –2xy + 7y² – 10x – 10y – 7 = 0
• D. 7x² – 2xy + 7y² + 10x + 10y – 7 = 0

Answer 1

Answer: (A)

7x² + 2xy + 7y² + 10x – 10 y + 7 = 0

Answer 2

Apply SP/PM = e. (by definition) SP/PM = 1/2

̃ 4(SP)²=PM²̃ 4{(h+1)²+(k1)²}

=$\{|h - k + 3/\sqrt{2}|\}^{2}$

̃ 7x²+2xy+7y²+10x–10y+ 7 = 0