Question

Find the equation of the ellipse whose focus is (1,0) the directrix is x+y+1=0 and eccentricity is 1/√2

Answer 1

Step-by-step explanation:

Let S be the focus of the ellipse and e be the eccentricity of the ellipse.

Consider that P(x,y) be any point on the ellipse, then by the definition of ellipse,

SP=e×PM

(x−1)2+(y−0)2=21(12+12x+y+1)

(x−1)2+(y)2=21(x+y+1)

(x−1)2+(y)2=41(x+y+1)2

3x2+3y2−2xy−10x−2y+3=0

The required equation of ellipse is 3x2+3y2−2xy−10x−2y+3=0.

Answer 2

Answer:

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Step-by-step explanation:

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