Is the origin and is a fixed point on the circle of radius with centre

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

O

is the origin and

A

is a fixed point on the circle of radius

a

with centre

O

. The vector

\mathbf{OA}

is denoted by

\mathbf{a}

. A variable point

P

lie on the tangent at

A

and

\mathbf{OP} = \mathbf{r}

. Show that

\mathbf{a} \cdot \mathbf{r} = a^2

. Hence, if

P(x, y)

and

A(x_1, y_1)

deduce the equation of tangent at

A

to this circle.