Question

Using the following equation, find the center and radius:
x2 + 2x + y2 + 4y = 20


The center is located at (1, 2), and the radius is 25.

The center is located at (-1, 2), and the radius is 25.

The center is located at (-1, -2), and the radius is 5.

The center is located at (1, 2), and the radius is 5.

Answer 1

@LynFran

Answer 2

HI!!

Answer 3

this is a job for "completing the square"
you have to do it twice, once for \(x^2+2x\) and again for \(y^2+4y\)
it is not too hard
do you know how to do it?

Answer 4

no

Answer 5

ok lets start with
\[x^2+2x\]
what is half of 2?

Answer 6

1

Answer 7

right
and now what is \(1^2\_?

Answer 8

1

Answer 9

oops
what is \(1^2\)?

Answer 10

ok so we turn \[x^2+2x\] in to \[(x+1)^2\] and add 1 to the other side making it
\[(x+1)^2+y^2+4y=21\]

Answer 11

now repeat with \(y^2+4y\)
what is half of 4?

Answer 12

2

Answer 13

ok and \(2^2\)?

Answer 14

2

Answer 15

hmm no

Answer 16

sorry 4

Answer 17

right
so turn \(y^2+4y\) in to \((y+2)^2\) and add 4 to the other side

Answer 18

now we are at
\[(x+1)^2+(y+2)^2=25\] and from that you can read off the center and the radius as it is in standard form for a circle

Answer 19

you good from there?

Answer 20

Yea so the answer is (-1,-2) radius 5?

Answer 21

yes

Answer 22

thx

Answer 23

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Answer 24

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