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

The equation of an ellipse is given by,

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

Hence,

Cross multiplying we get,

Multiply by 4 on both sides,

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

Substituting this,

Cross multiply,

Subtracting equations 2 and 1,

Substituting in 2,

Substituting the values in the equation for ellipse,

Multiplying whole equation by 32 we get,

3x² + 5y² = 32

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4