If (-2, m) is on a circle with center C (2, 3) and radius 4, what is the value of m?

The answer is d. m=3

We know that the equation of a circle is defined as:

x² + y² = r², where the origin is the centre.

Hence, with a centre of (2, 3) and radius of 4 becomes:

(x-2) ² + (y-3) ² = 4²

Expanding that out, we get:

x² - 4x + 4 + y² - 6y + 9 = 16

x² - 4x + y² - 6y - 3 = 0

Substitute x = - 2 as (-2, m) satisfies this equation.

(-2) ² - 4 (-2) + y² - 6y - 3 = 0

4 + 8 + y² - 6y - 3 = 0

y² - 6y + 9 = 0

Hence, (y - 3) ² = 0

y - 3 = 0

And y = 3

So, at x = - 2, m = 3