Question

find the equation of ellipse whose focus is (3,0) and directrix is X = 5 and eccentricity=2/3​

Answer 1

Answer:

Let P≡(h,k) be moving point e=

PM

PS

=

2

1

⇒(h+1)

2

+(k−1)

2

=

4

1

(

2

h−k+3

)

2

⇒ locus of P(h, k) is 8(x

2

+y

2

+2x−2y+2)=(x

2

+y

2

−2xy+6x−6y+9)

7x

2

+7y

2

+2xy+10x−10y+7=0