Well I'm kinda stumped and I need you guys...
1.) The length of a diameter of a circle described by 9x^2 + 9y^2 = 16 is?
2.) Find the equation of the circle with center on x+y = 4 and 5x+2y+1=0 and having a radius of 3.
Regarding #2:
The equation for a circle with center (h,k) and radius r is:
.
So you know r = 3. Where's the center?
Recall that it lies on the two lines given, so find the intersection of the two lines. I did it by substitution, starting with the first equation, which gives:
.
Sub this into the other equation for y, which gives:
.
Recall , so .
So your center is at . Now you know h, k, and r, the three essentials for writing the equation of a circle.
There you are!