Question

# The equation of the conic with focus at (1, –1), directrix along x – y + 1 = 0 and with eccentricity √2 is

A

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B

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C

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D

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Solution

## The correct option is D If (x1,y1) is a point on the conic, then √(x1−1)2+(y1−1)2=√2∣∣∣x1−y1+1√2∣∣∣⇒(x1−1)2+(y1+1)2=(x1−y1+1)2⇒x21+1−2x1+y21+1+2y1=x21+y21−2x1−2y1+1⇒2x1y1−4x1+4y1+1=0 ∴ The equation of the conic is 2xy−4x+4y+1=0

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