Question

Which point is on the circle described by (x - 2)2 + (y + 3)2 = 4?

Answer 1

when x=0 y= -3

Answer 2

x-a)^2+(y-b)^2=R^2 is the point M(a,b) and the radius of this circle is R
(x – 2)^2 + (y + 3)^2 = 17 the center of this circle is A(2,-3)and the center of the circle (x – 5)^2 + y^2 = 32 is B(5,0)
The line (D): y=ax+b which passes through A and B is such that
A belongs to (D) ==> -3=a(2)+b=2a+b ==> b=-2a-3(*)
B belongs to (D) ==> 0=a(5)+b=5a+b ==>b=-5a(**)
(*) and (**) lead to -5a=-2a-3 ==> 5a-2a-3=0 ==> 3a-3=0 ==>3a=3
==> a=3/3=1 ==> a=1 From (**) b=-5a=-5(1)=-5
Finally the equation of (D) is y=x-5

Answer 3

This (when x=0 y= -3) is the y-intercept of the circle.