# How do you find the equation for the circle if the equation of two diameters are 2x+y=6 and 3x+2y=4 and radius is 9?

Aug 27, 2016

${\left(x - 8\right)}^{2} + {\left(y + 10\right)}^{2} = {9}^{2}$

#### Explanation:

The two diameters will meet at the centre of the circle
$2 x + y = 6$
Or
$4 x + 2 y = 12$

And

$3 x + 2 y = 4$

Subtract gives x =8
Substitute in one equation gives y=-10

Then check that you are right in the other equation

The general equation of a circle is ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$
Where (a,b) is the centre of the circle and r is the radius.

The centre of the circle is (8,-10) the radius is 9