Question

Show that the equation of a tangent to the circle x² + y² = a² at the point P(x₁,y₁) on it is xx₁ + yy₁ = a²

Answer 1

Given equation of circle is x² + y² = a²

Differentiating w.r.t. x, we get

`2x + 2y dy/dx = 0`

∴ `dy/dx = -x/y`

Slope of the tangent at P(x₁, y₁)

= `(dx/dy)_((x_1,y_1)) = - x_1/y_1`

Equation of a tangent to the circle at P(x₁, y₁) is