Question

Find the equation of the ellipse whose one of the foci is (2,0) and the corresponding directrix is x = 8 and e=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=0.

Step-by-step explanation: