The Equation Of The Ellipse Whose Axes Are Of Lengths 6 And and Their Equations Are x – 3y + 3 = 0 And 3x + y – 1 = 0 Respectively, Is

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Question

The equation of the ellipse whose axes are of lengths 6 and and their equations are x – 3y + 3 = 0 and 3x + y – 1 = 0 respectively, is

diffcult

Solution

Correct option is

Let P(x, y) be nay point on the ellipse and let p₁ and p₂ be the lengths of the perpendiculars draw from P on the major and minor axes of the ellipse. Then,

Let 2a and 2b be the lengths of the major and minor axes of the ellipse,

We have,

The equation of the ellipse is