Question

In Cartesian coordinates, the point A is (x₁, y₁) where x₁ = 1 on the curve y = x² + x + 10. The tangent at A cuts the x-axis at B. Then find the value of the dot product vector OA . AB.

Answer 1

Given curve is

y = x² + x + 10

When x = 1. Then

y = 1² + 1 + 10 = 12

Therefore

A = (1, 12)

⇒ vector OA = i + 12j

From Eq. (1), we get

dy/dx = 2x + 1

Equation of tangent at A is

Therefore,

y = 3(x + 3)

This tangent cuts x-axis (that is, y = 0) at (−3, 0). Therefore,