Question

Select the correct answer. Which point lies on the circle represented by the equation (x + 7)2 + (y − 10)2 = 132? A. (5,12) B. (-7,-3) C. (-6,-10) D. (6,23)

Answer 1

B. (-7,-3)

Explanation:

Given the circle:
`(x + 7)^2 + (y - 10)^2 = 13^2`

The point (x,y) which lie on the circle are the coordinate which satisfies the given equation of the circle.

We now consider the given options.

Option A (5,12)

When x=5, y=12

`(5 + 7)^2 + (12 - 10)^2 =12^2+2^2=148\\eq 169= 13^2`

Option B (-7,-3)

When x=-7, y=-3

`(-7 + 7)^2 + (-3 - 10)^2 =0^2+(-13)^2= 169=13^2`

Option C (-6,-10)

When x=-6, y=-10

`(-6 + 7)^2 + (-10 - 10)^2 =1^2+(-20)^2=401\\eq 169= 13^2`

Option D (6,23)

When x=6, y=23

`(6 + 7)^2 + (23 - 10)^2 =13^2+13^2=338\\eq 169= 13^2`

We can see that only (-7,-3) satisfies the equation of the circle. Thus it is the point which lies on the circle.

The correct option is B.