Question

Find the equation of the ellipse, with major axis along x axis and passing through the points (4,3) and (-1,4).

Answer 1

Step by step Explanation:

Equation of an ellipse is given by,

x2a2+y2b2=1

As the ellipse, passes through (4,3),

∴16a2+9b2=1

Let 1a2=pand1b2=q, then,

⇒16p+9q=1→(1)

As the ellipse, passes through (6,2),

∴36a2+4b2=1

⇒36p+4q=1→(2)

Multiplying (2) by 94 and then, subtracting (1) from it,

81p+9q−16p−9q=94−1

⇒65p=54⇒p=152

Putting value of p in (1),

1652+9q=1

⇒9q=3652⇒q=452⇒q=113

∴1a2=152and1b2=113

Putting these values in the equation of the ellipse,

x252+y213=1, which is the required equation.

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