Q. 164.0( 2 Votes )

# Find the eq

Answer :

Given that we need to find the equation of the ellipse whose distance between the foci is 8 units and distance between the directrices is 18 units. We know that the distance between the foci is 2ae.

2ae = 8

ae = 4 ..... - (1)

We know that the distance between the directrices is .  ..... - (2)

(1)×(2) a2 = 36 .... (3)

a = 6

We know that eccentricity of an ellipse is  36 - b2 = 16

b2 = 20 ..... (4)

The equation of the ellipse is,  5x2 + 9y2 = 180

The equation of the ellipse is 5x2 + 9y2 = 180.

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