# circle problem

• Apr 22nd 2010, 12:56 PM
circle problem
Hello everyone!

I am having problems solving a simple circle, problem, I would appreciate any help/guidance as I wasn't provided with references, so I'm having trouble solving this problem because I have no knowledge of the concepts! If someone could some me how to solve this problem I'd be grateful!

Find the centre and radius of the circle
X(Squared) + y(Squared) + 2x - 8y + 8 = 0
Find the centre and radius of the another circle which touches the y-axis at the origin and passes through (4, 2)
Compute the distance between the centres of the two circles, and whether they intersect at one point, two points or no points.
Find the parametric equations of the first circle. (what does parametric even mean?)

Regards,
• Apr 22nd 2010, 01:16 PM
TKHunny
Quote:

Find the centre and radius of the circle
X(Squared) + y(Squared) + 2x - 8y + 8 = 0

Not nuch sense doing the others if you can't do this one.

When faced with this:

$x^{2} + 2x = 0$

Use "Completing the Square" to put it in this form:

$(x-h)^{2} = b$
• Apr 22nd 2010, 01:25 PM
How? the best I can come up with is x(x+2) + y(y-8)+8=0 is that correct? what's the next step?
• Apr 22nd 2010, 08:18 PM
sa-ri-ga-ma
Quote:

How? the best I can come up with is x(x+2) + y(y-8)+8=0 is that correct? what's the next step?

No. this is not the step.
You have to rewrite the equation in the form of
(x-h)^2 + (y-k)^2 = r^2.
So
x^2 + 2x + 1 + y^2 - 8y + 16 + 8 - 17 = 0
Can you proceed now?
• Apr 23rd 2010, 08:09 AM
Thanks! I came up with (x + 1)^2 + (y - 4)^2 = 9^2; therefore my center would be (1, -4) and my radius would be 9. correct? What about next question?
• Apr 23rd 2010, 08:25 AM
sa-ri-ga-ma
Quote:

Thanks! I came up with (x + 1)^2 + (y - 4)^2 = 9^2; therefore my center would be (1, -4) and my radius would be 9. correct? What about next question?

The value of he radius is wrong.

(x + 1)^2 + (y - 4)^2 = 9^2;

This should be (x + 1)^2 + (y - 4)^2 = 3^2;
For the second problem, the center lies on the x-axis. And its co-ordinates is (h, 0). So its radius is h. Find the distance between (h, 0) and the given point (4, 2) and equate it to h. Then solve for h.
• Apr 23rd 2010, 09:25 AM
Alright! great! what about finding the "parametric equation" of the first circle, which we already found the center of (1, -4) and r = 3 ?

and with regards to finding the distance between (h,0) and (4,2) how should I approach it? what should I apply? what formula?
• Apr 23rd 2010, 10:08 AM
masters
Quote:

Alright! great! what about finding the "parametric equation" of the first circle, which we already found the center of (1, -4) and r = 3 ?

Your center should be at (-1, 4), not (1, -4).

$x=a+r \cos t$

$y=b+r \sin t$

where a and b are the coordinates of the center,
r is the radius, and t is a parametric variable interpreted
geometrically as the angle that the ray from (a, b) to (x, y) makes with the polar axis.
• Apr 23rd 2010, 10:13 AM