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

Answer:

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

=

2

1

(

1

2

+1

2

x+y+1

)

(x−1)

2

+(y)

2

=

2

1

(x+y+1)

(x−1)

2

+(y)

2

=

4

1

(x+y+1)

2

3x

2

+3y

2

−2xy−10x−2y+3=0

The required equation of ellipse is 3x

2

+3y

2

−2xy−10x−2y+3=O

Answer 2

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