Q. 5 E5.0( 5 Votes )

# find the eq

Given that we need to find the equation of the ellipse passing through the points (1,4) and (- 6,1).

Let us assume the equation of the ellipse as (a2>b2). ..... .... (1)

Substituting the point (1,4) in (1) we get

b2 + 16a2 = a2 b2 ..... - - (2)

Substituting the point (- 6,1) in (1) we get

a2 + 36b2 = a2b2 ..... - - (3)

(3)×16 - (2)

(16a2 + 576b2) - (b2 + 16a2) = (16a2b2 - a2b2)

575b2 = 15a2b2

15a2 = 575

From (2)

The equation of the ellipse is

3x2 + 7y2 = 115

The equation of the ellipse is 3x2 + 7y2 = 115.

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