Thread: Circle

Write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k).

(1) GIVEN:

r = 3; (h, k) = (1, 0)

(2) GIVEN:

r = 3; (h, k ) = (0, 0)

(3) Graph each circle on the SAME xy-plane.

NOTE: When (h, k) is given, does it mean that the circle has been moved from the origin (0,0)?

Originally Posted by symmetry

Write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k).

(1) GIVEN:
r = 3; (h, k) = (1, 0)

(2) GIVEN:
r = 3; (h, k ) = (0, 0)

(3) Graph each circle on the SAME xy-plane.
NOTE: When (h, k) is given, does it mean that the circle has been moved from the origin (0,0)?

Hello,

I'll be probably too late, because alle the big shots are online, but nevertheless I'l give it a try:

With a circle in the x-y-plane you have 2 different equations:
(1) or
(2)

You can easily transform (1) into (2) by expanding the brackets and collecting the constants.


to (1):


to (2)


to (NOTE)
Correct: The h-value indicates a translation in x-direction, the k-value indicates a move in y-direction.

h<0: move left, h>0: move right.
k<0: move up, k>0: move down

If you use another equation of the circle, the last properties may change, be careful with those signs in the brackets.

EB

You said:

"The h-value indicates a translation in x-direction, the k-value indicates a move in y-direction."

AND

"h<0: move left, h>0: move right.
k<0: move up, k>0: move down."

This is very useful data for students and teachers.

I thank you very much.