Question

I need to write the standard form of the equation of the circle with the given center and radius.
center (7, -4) and r = 5

Answer 1

kinda forgot what standard form was............

Answer 2

The standard form equation of a circle is a way to express the definition of a circle on the coordinate plane.

Answer 3

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

Answer 4

I am confused?

Answer 5

(x-7)^2+(y+4)^2=5^2

Answer 6

The standard equation with the centre (a,b) and the radius r is :
\[\Large(x-a)^2+(y-b)^2=r^2\]

Answer 7

so you recognize the equation @violetanna ??

Answer 8

on @Noura11 's equation the a and b represent the center points and r represent the Radius. Do you get that so far?

Answer 9

yup

Answer 10

Okay

Answer 11

so would that be the standard form :(x-7)^2+(y+4)^2=5^2

Answer 12

or so I simplify it.....

Answer 13

simplify it

Answer 14

(x-7)^2+(y+4)^2=25

Answer 15

x^2-49+y^2+16=25

Answer 16

x^2+y^2-33=25

Answer 17

no, you can't simplify it like that

Answer 18

x^2+y^2=58

Answer 19

y not?

Answer 20

because you can only go up to (x-7)^2+(y+4)^2=25 in simplifying a Standard or General Form of the Circle's Equation

Answer 21

ok got it

Answer 22

okay hold on. I made a mistake, if you want the general form of equation you simplify more but if you want the standard you stick you (x-7)^2+(y+4)^2=25

Answer 23

okay?

Answer 24

I wanted standard Thank you so much!!!

Answer 25

Your welcome! Here is an example so you would understand it more.

r = 5; (h, k) = (-5, 2)
General Form:
x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0
x^2 + y^2 - 2(-5)x - 2(2)y + (-5)^2 + 2^2 - 5^2 = 0
x^2 + y^2 + 10x - 4y + 25 + 4 - 25 = 0
x^2 + y^2 + 10x - 4y + 4 = 0 ANS

Standard Form:
(x - h)^2 + (y - k)^2 = r^2
(x - -5)^2 + (y - 2)^2 = 5^2
(x + 5)^2 + (y - 2)^2 = 25 ANS

Answer 26

So don't worry about general now. Standard is easy!

Answer 27

wait so my final answer was (x-7)^2+(y+4)^2=25

Answer 28

is that wrong?

Answer 29

No, its right!

Answer 30

I was just giving you an example, did I confuse you???

Answer 31

awesome