Question

In the XY-Plane above, the circle has center (h,k) and radius 10. What is the value of k?

Answer 1

k = +/- 6

Explanation:

In the XY-Plane above, the circle has center (h,k) and radius 10. What is the value of k?

The concluding part of this question will be

Two coordinates are given, (4,0) and (20,0)

equation of a circle

(
`(x-h)^(2) +(y-k)^(2) =r^(2)`

We can then have two equations of the circle and solve simultaneously

(
`(4-h)^(2) +(-k)^(2) =10^(2)` .............................1

(
`(20-h)^(2) +(-k)^(2) =10^(2)` ......................................2

combining the two equation to solve

(20-h)^2 - (4-h)^2 = 0

20^2 - 40h +h^2 -4^2 + 8h -h^2 = 0

20^2 - 42 = 32h

h = 12

(4-12)^2 + (-k)^2 = 100

k^2 = 36

k = +/- 6