Question

show that the equation 4x^2+4y^2-4x-12y+1=0 represents a circle. find its center and radius

Answer 1

You need to complete to square for your x's and your y's to put it into standard form for a circle.

Answer 2

get in in the form: (x-a)^2 + (y-b)^2 = r^2

where r is the radius, and (a,b) the center

Answer 3

First, divide each term by 4

Answer 4

\[x^2-x+y^2-3y=-\frac{1}{4}\]

Answer 5

Now add 1/4 and 9/4 to the x an y parts respectively and to the right side

Answer 6

k i divided each term by 4 and i got \[x^2+y^2+x-3y+1/4=0\] am i ryt?

Answer 7

\[x^2+x+\frac{1}{4}+y^2-3y+\frac{9}{4}=-\frac{1}{4}+\frac{1}{4}+\frac{9}{4}\]

Answer 8

Now factor the two trinomial squares and add the like terms to determine the center and radius.

Answer 9

k could u pls explain how u got 9/4?

Answer 10

The y coefficient is 3. (1/2)(3)=3/2 and (3/2)^2=9/4

Answer 11

k what do i do next to get center nd radius?

Answer 12

Now factor the two trinomial squares and add the like terms to determine the center and radius.

Answer 13

k i got x^2+y^2+x-3y+5/2=-5/2 am i ryt?

Answer 14

mertsj how do i find center and radius from here

Answer 15

\[(x+\frac{1}{2})^2+(y-\frac{3}{2})^2=\frac{9}{4}\]

Answer 16

Center is (-1/2, 3/2) Radius is 3/2

Answer 17

how did get it