If a tangent to the circle x 2 + y 2 = 1 intersects the coordinate axes at distinct points P and Q , then the locus of the mid-point of P Q is:

Step-by-step solution

Any point on the circle x 2 + y 2 = r 2 is r cos θ ,   r sin θ and the equation of the tangent at this point is x cos θ + y sin θ = r . Thus, any point on circle x 2 + y 2 = 1 is cos θ ,   sin θ and the equation of tangent at this point is x cos θ + y sin θ = 1 . To find the point where this line intersects the x -axis, put y = 0 , ⇒ x = 1 cos θ   ⇒ P = 1 cos θ ,   0 And, to find the point where this line intersects the y -axis, put x