Analytic Geometry Homework

• Mar 3rd 2008, 12:54 AM
valcross
Analytic Geometry Homework
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.
• Mar 3rd 2008, 08:21 AM
Simplicity
Quote:

Originally Posted by valcross
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?

1)

$\displaystyle 9x^2 + 9y^2 = 16$
$\displaystyle x^2 + y^2 = \frac{16}{9}$
As general form is $\displaystyle x^2 + y^2 = r^2$
$\displaystyle \implies r^2 = \frac{16}{9}$
$\displaystyle r = \frac{4}{3}$
$\displaystyle \therefore d=\frac{8}{3}$
• Mar 3rd 2008, 09:13 AM
Mathnasium
Regarding #2:

The equation for a circle with center (h,k) and radius r is:

$\displaystyle (x-h)^2 + (y-k)^2 = r^2$.

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:

$\displaystyle y=4-x$.

Sub this into the other equation for y, which gives:

$\displaystyle 5x+8-2x+1=0$

$\displaystyle 3x+9=0$

$\displaystyle 3x=-9$

$\displaystyle x=-3$.

Recall $\displaystyle y=4-x$, so $\displaystyle y=4-(-3)=7$.

So your center is at $\displaystyle (-3,7)$. Now you know h, k, and r, the three essentials for writing the equation of a circle.

There you are!
• Mar 4th 2008, 01:16 AM
valcross
Thanks guys, that was very educational, not to mention I now have my homework done thanks to you.