Question

Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle.
x^2+y^2-1/4x+1/4y=7/32

Answer 1

Well, do it. You will need to "Complete the Square", twice.

x^2 - (1/4)x + _____ + y^2 + (1/4)y + ____ = (7/32) + _____ + ____

Go!

Answer 2

I need help

Answer 3

You're saying you do not know how to "Complete the Square"?

Answer 4

no i do

Answer 5

let me do it

Answer 6

Excellent. Let's see what you get. I rearranged it a little more conveniently for you up above.

Answer 7

How do I not put it in decimal form?

Answer 8

Simply don't.

x^2 - (1/4)x + _____ + y^2 + (1/4)y + ____ = (7/32) + _____ + ____

(1/2)*(1/4) = 1/8
(1/8)^2 = 1/64

This gives:

x^2 - (1/4)x + (1/64) + y^2 + (1/4)y + ____ = (7/32) + (1/64) + ____

How about the other one?

Answer 9

y^2+1/4y+1/64

Answer 10

Okay, now we have

x^2 - (1/4)x + (1/64) + y^2 + (1/4)y + (1/64) = (7/32) + (1/64) + (1/64)

What's next? There should be some significant simplification or we just failed to make any sense at all.

Answer 11

for the right side I go =1/4

Answer 12

7/32 + 1/64 + 1/64 = 7/32 + 2/64 = 7/32 + 1/32 = 8/32 = 1/4 Okay, I'll bite.

How about the left-hand side?

Answer 13

I am not quite sure

Answer 14

What was the point of "Completing the Square"?

Answer 15

To get the factors

Answer 16

No, it was to make perfect squares!

y^2+1/4y+1/64 = (y + 1/8)^2

Do that with the x and write the whole thing. You'll be almost done.

Answer 17

so it would be (x-1/8)^2

Answer 18

Yes. Now, we are ready to answer all the Problem Statement asks.

(x - 1/8)^2 + (y + 1/8)^2 = 1/4

This certainly looks like a circle to me.

What is the Center?
What is the Radius?

Answer 19

center= 1/8, -1/8

Answer 20

radius= (1/4)

Answer 21

wait or is the radius the square root of 1/4?

Answer 22

You got it!!! I deliberately failed to write it in the proper form, just to see if you were paying attention.

(x - 1/8)^2 + (y + 1/8)^2 = (1/2)^2

Now, it's a bit more obvious.

Answer 23

YAY!
Thank you so much!!

Answer 24

Good work.

Recognizing the standard form was the important part of the problem.
Completing the square was the important process to get us there.