SOLUTION: A circle has its center at(4,0) and a radius of 5 units. Which quadrants does the circle pass through.

Question 596072: A circle has its center at(4,0) and a radius of 5 units. Which quadrants does the circle pass through.
Found 2 solutions by Alan3354, math-vortex:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A circle has its center at(4,0) and a radius of 5 units. Which quadrants does the circle pass through.
--------------
All 4
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
.
This circle passes through all four quadrants. Here's why:
.
[I] Quadrant I
The center of this circle is at (4,0) on the x-axis. Since the radius is 5 units, every point on the circle is exactly 5 units from (4,0). The point (4,5) is 5 units directly above (4,0). We can see that (4,5) is in quadrant I because the x- and y-coordinates are both positive.
.
.
{II}Quadrant IV
Using similar reasoning, the point (4,-5) is 5 units directly below (4,0). We can see that (4,-5) is in Quadrant IV because the x-coordinate is positive, and the y-coordinate is negative.
.
.
[III] Quadrant II
We can use the distance formula to show that the circle passes through these quadrants. The point (-1,0) is 5 units directly to the left of (4,0). Let's choose an x-coordinate between 0 and -1, say -0.5. We'll use the distance formula to find the y-coordinate of the point that is exactly 5 units from the center, (4,0).
.

.
Now, solve for y. Square both sides of the equation.

.
The square root of 5.64 is a positive number, about 2.4. We know that the point (-0.5, sqrt(5.64)) is in Quadrant II because the x- and y-coordinates are positive, negative, respectively.
.
.
Quadrant III
The point (-0.5,-sqrt(5.64)) is also exactly 5 units from (4,0). Try it in the distance formula above to see that this is the case. This point is in Quadrant III because both coordinates are negative.
.
Hope this helps! Feel free to email if you have questions about the explanation.
.
Ms.Figgy
math.in.the.vortex@gmail.com
RELATED QUESTIONS
The graph of a circle has its center at (2,3) with a radius of 10 units. Which point does (answered by reviewermath)
A circle has its center at (-4,5) and a radius of 7 units. What is the equation of the... (answered by Alan3354)
A circle has its center at (-4, -2) and is tangent to the line 3x+4y-5=0. What is the... (answered by josgarithmetic)
A unit circle has its center at (5,0) and a second circle with a radius of 2 units has... (answered by ikleyn)
If the radius of a circle is 4 units and its center (0;0),what is the equation of the... (answered by Alan3354)
Suppose x is any positive number. Circle 1 has a center at (1, −6) and a radius of (answered by Edwin McCravy,ikleyn)
Which is an equation of the circle with a radius of 9 units and center at (�4, 2)? (answered by ewatrrr)
Given the equation of the circle (x - 9) 2 + y 2 = 484, the center of the circle is... (answered by solver91311)
Given the equation of the circle (x � 9)2 + y2 = 484, the center of the circle is located (answered by solver91311)