Question

Circle C has a center of (-2, 3) and a radius of 4. Does point (-4, 6) lie on circle C?

Answer 1

(-4, 6) does not lie on circle C

Explanation:

The given circle has a center of (-2, 3) and a radius of 4.

The equation of this circle is given by

`{(x - a)}^(2) + {(y - b)}^(2) = {r}^(2)`

where (a,b) is the center.

This implies that:

`{(x + 2)}^(2) + {(y - 3)}^(2) = {4}^(2)`

If the point (-4,6) lies on this line, then it must satisfy this equation.

`{( - 4 + 2)}^(2) + {(6 - 3)}^(2) = {4}^(2)`

`{( - 2)}^(2) + {(3)}^(2) = {4}^(2)`

`4 + 9 = 16`

This statement is false hence (-4,6) does not lie on this circle