The circle, question help!!!?

Question

1) State the centre and the radius of the circle defined by
(x – 2)2 + (y + 3)2 = 36.
2. Determine whether the following points lie on the circle defined by
(x + 1)2 + (y + 2)2 = 13.
a) (1,-5)
b) sqrt3-1,sqrt10-2
c) (-1, -2)
 

Answer 1

1) Given equation of a circle (x - 2)^2 + (y +3)^2 = 36

Standard equation of a circle (x - h)^2 + (y - k)^2 = r^2

For standard equation of circle centre = (h , k) and radius = r

Compare the given equation of circle with standard equation of circle

Here h = 2 and k = -3 and r = sqrt(36)

Therefore centre = (2 , -3) and radius = sqrt(36) = 6

2) (x+1)^2+(y+2)^2 = 13

a)(1, -5)

Substitute the (1,-5) in given equation.

(1+1)^2+(-5+2)^2 = 13

2^2+-3^2 = 13

4+9 = 13

13 = 13

The point lies on the circle

b)(√2,√8)

(√2+1)^2+(√8+2)^2 = 13

2+1+2√2+8+4+4√8 = 13

15+2√2+4√8 = 13

.c) (-1, -2)

(-1+1)^2+(-2+2)^2 = 13

0+0 = 13

Other two points b,c  not satisify the given circle equation.

Option a is correct answer.