# The equation of a circle is 3x^2 + 3y^2 -2x +my - 2 = 0. What is the value of m if the point (4,3) lies on the circle?

##### 1 Answer
Jul 28, 2016

$m = - \frac{65}{3}$

#### Explanation:

Substitute $x = 4$, $y = 3$ into the equation to find:

$3 \left({4}^{2}\right) + 3 \left({3}^{2}\right) - 2 \left(4\right) + m \left(3\right) - 2 = 0$

That is:

$48 + 27 - 8 + 3 m - 2 = 0$

That is:

$3 m + 65 = 0$

So $m = - \frac{65}{3}$

graph{(3x^2+3y^2-2x-65/3y-2)((x-4)^2+(y-3)^2-0.02) = 0 [-8.46, 11.54, -2.24, 7.76]}