Question

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?

Answer 1

`(x-8)^2+(y+10)^2=9^2`

Explanation:

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

And

`3x+2y=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 `(x-a)^2+(y-b)^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

Hence the answer