A circle is centered at C(−1,−3) and has a radius of 6.Where does the point P(-6,-6) lie?

Question

asked Nov 24, 2019 143k views

2 Answers

MattyP · Answer 1 · 2019-11-30T21:33:46+0000

The equation of circle is

(x-h)^(2) + (y-k)^(2) = r^(2) . -------- (h, k) is the center of the circle.

The point is inside the circle if the distance from it to the centre is less than the radius. Symbolically, this is

$\sqrt{({x - h})^(2) +{(y - k)}^(2)} < r$

and point is outside the circle if the distance from it to the centre is great than the radius. Symbolically, this is

$\sqrt{({x - h})^(2) +{(y - k)}^(2)} > r$

and if this distance is equal to r then it lies on the cirlce.Symbolically, this is

$\sqrt{({x - h})^(2) +{(y - k)}^(2)} = r$

now by putting the value of (x , y) and (h,k)

$\sqrt{(-6 - -1)^(2) + (-6 - -3)^(2)}$

=√(25 + 9)

=√(34)

since our r is 6 and

=5.8 < 6

So the point (-6 , -6) is inside the circle.