Find the equation of the normal to the curve x 2 + 2y 2 – 4x – 6y + 8 = 0 at the point whose abscissa is 2

Question

Philoid · Accepted Answer

finding slope of the tangent by differentiating the curve

Finding y co – ordinate by substituting x in the given curve

2y² – 6y + 4 = 0

y² – 3y + 2 = 0

y = 2 or y = 1

m(tangent) at x = 2 is 0

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at x = 2 is , which is undefined

equation of normal is given by y – y₁ = m(normal)(x – x₁)

x = 2