Question

Find k, if the line 2x − 3y + k = 0 touches the ellipse 5x² + 9y² = 45.

Answer 1

Equation of the ellipse is 5x² + 9y² = 45.

i.e `x^2/9 + y^2/5 = 1`

Comparing this equation with `x^2/a^2 + y^2/b^2 =  1`, we get

a² = 9, b² = 5

The equation of tangent is 2x − 3y + k = 0.

∴ k² = 81

∴ k = ± 9