First slide

Definition of a circle

Question

The inverse point of $(1, - 1)$ with respect to $x^{2} + y^{2} = 4$ , is

Moderate

A

$(- 1, 1)$
B

$(- 2, 2)$
C

$(1, - 1)$
D

$(2, - 2)$

Solution

We know that two points are inverse points with respect to a circle if each lies on the polar of the other. The polar of (1, -1) with respect to $x^{2} + y^{2} = 4$ is $x - y = 4$
Clearly, (2, - 2) lies on it. Hence, the inverse point of (1, -1) with respect of $x^{2} + y^{2} = 4$ is (1,-1).

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