Q.6. The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (-3, 1) and (2,-2) is
(A) 5x2 + 3y =32 (B) 3r? + 5y = 32 (C) 5x° - 3y2 = 32 (D) 3x* + 5y? + 32 = 0

Equation of the ellipse = 3x² + 5y² = 32

Step-by-step explanation:Given:The centre of the ellipse is at the origin and the X axis is the major axisIt passes through the points (-3, 1) and (2, -2)To Find:The equation of the ellipseSolution:

The equation of an ellipse is given by,

Given that the ellipse passes through the point (-3, 1)

Hence,

Cross multiplying we get,

9b² + a² = 1 ²× a²b²a²b² = 9b² + a²

Multiply by 4 on both sides,

4a²b² = 36b² + 4a²------(1)

Also by given the ellipse passes through the point (2, -2)

Substituting this,

Cross multiply,

4b² + 4a² = 1 × a²b²a²b² = 4b² + 4a²-------(2)

Subtracting equations 2 and 1,

3a²b² = 32b²3a² = 32a² = 32/3----(3)

Substituting in 2,

32/3 × b² = 4b² + 4 × 32/332/3 b² = 4b² + 128/332/3 b² = (12b² + 128)/332b² = 12b² + 12820b² = 128b² = 128/20 = 32/5

Substituting the values in the equation for ellipse,

Multiplying whole equation by 32 we get,

3x² + 5y² = 32

Hence equation of the ellipse is 3x² + 5y² = 32