What is the Center and Radius of a Circle?

  • #1
mathdad
1,283
1
A. Determine the center and radius of circle.

B. Also, find the y-coordinates of the points (if any) where the circle intersects the y-axis.

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  • #2
If the circle were to intersect the y-axis, then what would x be?
 
  • #3
Joppy said:
If the circle were to intersect the y-axis, then what would x be?

If the circle intersects the y-axis, the value of x is 0. True?
 
  • #4
RTCNTC said:
If the circle intersects the y-axis, the value of x is 0. True?

No. If the circle intersects the y-axis, the value of x is 0 at the point(s) of intersection.

We must be absolutely clear.
 
  • #5
Re: Center & Radius of Circle

Joppy said:
No. If the circle intersects the y-axis, the value of x is 0 at the point(s) of intersection.

We must be absolutely clear.

How is part B found?

- - - Updated - - -

Is my work for part A correct?
 
  • #6
Yes, part A is correct.

Part B asks you to find the coordinates of the points where the circle intersects the y-axis. Joppy led you to the conclusion that those points must have x= 0. Now put x= 0 in the equation of the circle to determine what y is.
 
  • #7
Part B

Let x = 0

x^2 + (y + 1)^2 = 20

(0)^2 + (y + 1)^2 = 20

(y + 1)^2 = 20

sqrt{(y + 1)^2} = sqrt{20}

y + 1 = 2•sqrt{5}

y = 2•sqrt{5} - 1

The y-coordinate is 2•sqrt{5} - 1.

Yes?

Is one the points of intersection for the circle
(0, 2•sqrt{5}-1)?
 
  • #8
At the point:



Your next step should be:



Hence:



And so the points of intersection of the given circle and the -axis are:



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  • #9
We should be able to convince ourselves that given the circle:



We then know these points are on the circle:

 
  • #10
MarkFL said:
We should be able to convince ourselves that given the circle:



We then know these points are on the circle:


Cool notes. Check your PM.
 

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