Question

Identify the center and radius for the following equation: (x+4)²+(y-7)²-4

Answer 1

rewrite the equation

\[(x + 4)^2 + (y - 7)^2 = 4\]

the general form of a circle is

\[(x - h)^2 + (y - k)^2 = r^2\]

(h, k) is the centre and r is the radius.

hope this helps... to identify the centre and radius.

Answer 2

@campbell_st thank you!! so is (x+4)^2+(y−7)^2=4 the final answer? or are there more steps after that

Answer 3

no just identify the values for h, k and r...

this is a nice neat question where its written in factorised form

sometimes you may need to complete the square for x and y to find the centre and radius.

Answer 4

so what would the center & radius be in that case? @campbell_st

Answer 5

well what is the value of h=

when you look at your equation... ?

Answer 6

oh wait i think i get it now

Answer 7

so they both equal 4?

Answer 8

no the radius would be 2 since its squared?

Answer 9

ok... you are comparing

-h = + 4

and

-k = - 7

what are the values of h and k..?

Answer 10

the radius value is correct...

Answer 11

what would the center be then? if -h=4?

Answer 12

i don't know what positive h would be

Answer 13

-h = 4 so what is h...

just multiply both sides by -1

Answer 14

ohh thats right haha okay that was dumb
so h=-4

Answer 15

thank you so much

Answer 16

ok.. now what is k...?

Answer 17

7

Answer 18

correct so the centre is (-4, 7) and radius = 2

Answer 19

okay so for this problem: (x+1)²+(y+3)²=49 the center would be (1,-3) and the radius would be 7.. correct? thats what i got

Answer 20

@campbell_st

Answer 21

remember -h = 1 so h = -1 centre (-1, -3) and radius is 7...

good job

Answer 22

thanks so much

Answer 23

glad to help

Answer 24

can you possibly help me with another question similar to this? im not sure how to do it when the question is in a different format, ill post it now

Answer 25

ok... put it up