Question

The equation of the normal to the curve 2x² + y² = 12 at the point (2, 2) is ______.

Options

• 2x + y - 6 = 0

• x - 2y + 2 = 0

• 2x - y + 6 = 0

• x + 2y + 2 = 0

Answer 1

The equation of the normal to the curve 2x² + y² = 12 at the point (2, 2) is x - 2y + 2 = 0.

Explanation:

Given curve, 2x² + y² = 12

`=> 4x + 2y "dy"/"dx" = 0`

`"dy"/"dx" = (- 2x)/y`

Slope of tangent at (2, 2) is

`("dy"/"dx")_(2,2) = (- 2(2))/2` = - 2

∴ Slope of Normal = `- "dx"/"dy" = 1/2`

Equation of normal at (2, 2) is

`y - 2 = 1/2 (x - 2)`

⇒ 2y - 4 = x - 2

⇒ x - 2y + 2 = 0