Question

The inverse point of (1,-1) with respect to circle x² + y² =4 is
a) (-1,1)
b) (-2,2)
c) (1.-1)
d) (2,-2)​

Answer 1

Answer:

d) (2,-2)

Step-by-step explanation:

S:x

2

+y

2

=4

As we can see that P(1,−1) lies inside circle S

∵S

1

<0

Let Q(a,b) is a inverse point of P(1,−1) w.rt. x

2

+y

2

=4

then O(0,0) is the centre of circle S.

∴OP⋅OQ=r

2

=4

2

⋅OQ=4

OQ=2

2

...(1)

Equation of OP is y=−x

And Q lies on OP line

∴Q(a,−a) on line y=−x

⇒OQ=2

2

⇒a

2

=2

2

⇒a=2

∴ Inverse point of (1,−1) is Q(2,−2).

Hence, option D.