1. ## [ASK] Equation of a Circle

find standard eqations of circles that have centers on 4x+3y=8 and are tangent to both the line x+y=-2 and 7x-y=-6

What I got is $\displaystyle 4a=–4\pm3r\sqrt2$ and $\displaystyle b=4\pm r\sqrt2$. Dunno how to continue from here.

2. ## Re: [ASK] Equation of a Circle

the distance from the center $(a,b)$ of such a circle to a given straight line is equal to the radius $r$ of the circle

Furthermore $4a+3b=8$

3. ## Re: [ASK] Equation of a Circle

Yes, I did that. In fact, that was how I got to the aforementioned $\displaystyle 4a=–4\pm3r\sqrt2$ and $\displaystyle b=4\pm r\sqrt2$.

4. ## Re: [ASK] Equation of a Circle

Originally Posted by Monoxdifly
Yes, I did that. In fact, that was how I got to the aforementioned $\displaystyle 4a=–4\pm3r\sqrt2$ and $\displaystyle b=4\pm r\sqrt2$.
How did you get those equations? Show your work.

use $4a+3b=8$ to find $r$

The problem has two solutions.

5. ## Re: [ASK] Equation of a Circle

Originally Posted by Idea
How did you get those equations? Show your work.
By substituting 4a + 3b = 8 to the formula $\displaystyle y-b=m(x-a)\pm r\sqrt{1+m^2}$.