Question

Answer the following:

Find the equation of the tangent to the parabola y² = 9x at the point (4, −6) on it

Answer 1

The equation of the tangent to the parabola y² = 4ax at the point (x₁, y₁) is yy₁ = 2a(x + x₁)

The equation of the parabola is y² = 9x

Comparing this equation with y² = 4ax, we get,

∴ 4a = 9

∴ 2a = `9/2`

∴ the equation of the tangent to the given parabola at (4, – 6) is

y(– 6) = `9/2(x + 4)`

∴ – 2y = `3/2(x + 4)`

∴ – 4y = 3x + 12

∴ 3x + 4y + 12 = 0.