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O is the origin and A is a fixed point on the circle of radius 'a' with centre O.The vector `vec O A` is denoted by `vec a` . A variable point P lie on the tangent at `A and vec OP-vec r.` Show that `vec a vec r=a^2.`Hence if `P(x, y) and A(x_1, y_1),` deduce the equation of tangent at A to this circle.

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`xx_1+2yy_1=a`
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