Write the equation for the circle with center at (- 8, - 6) and radius of 10.
(x+8)² + (y + 6)² = 10
(x+8)² + (y + 6)² = 100
(x-8)² + (y - 6)² = 100
Find the standard equation for the circle with center on the positive x-axis and passing through the origin with radius of 2.
x² + y² = 4
(x + 2)² + y² = 4
(x - 2)² + y² = 4
Choose the appropriate description for the equation.
Given: 10(x - 3)2 + 10(y + 4)2 = 100
circle
point-circle
no circle
Choose the appropriate description for the equation.
Given: (x - 2)2 + (y + 3)2 = 49
circle
point-circle
no circle
Write the equation for the circle with center at (1, - 2) and passing through the origin.
(x - 1)² + (y + 2)² = 0
(x - 1)² + (y + 2)² = 5
(x - 1)² + (y + 2)² = 25
Choose the appropriate description for the equation.
Given: x2 + y2 = 0
circle
point-circle
no circle
Write the equation for the circle with center at (6,0) and radius of 6.
(x - 6)² + y² = 36
(x + 6)² + y² = 36
(x - 6)² - y² = 36
Write the equation for the circle with center at (0,0) and radius of 4.
x² + y² = 4
x² - y² = 16
x² + y² = 16
What is your questions about this test?
It is really easy.
if a,b is the center of a circle of radius r, then the equation is
(x-a)^2+(y-b)^2=r^2
You should memorize that.
It probably would be easy, but I don't have a teacher teaching me this. I do all my school work online and I just need this class to finish and graduate.
Write the equation of the circle centered at
(
−
8
,
6
)
with radius 16.
To write the equation for a circle, we need to use the standard form equation:
(x - h)² + (y - k)² = r²
where (h, k) represents the coordinates of the center of the circle and r represents the radius.
Now let's solve the given questions step by step:
1. Circle with center at (-8, -6) and radius of 10:
Using the standard form equation, we substitute the given values:
(x + 8)² + (y + 6)² = 10²
Simplifying further, we get:
(x + 8)² + (y + 6)² = 100
2. Circle with center on the positive x-axis and passing through the origin with radius 2:
Since the center is on the positive x-axis, the y-coordinate is 0. So the center is (h, k) = (x, 0). And the origin (0, 0) lies on the circle. Substituting these values into the equation:
(x - x)² + (y - 0)² = 2²
x² + y² = 4
3. Equation: 10(x - 3)² + 10(y + 4)² = 100
To determine if this is a circle equation, we divide both sides by 10 to simplify:
(x - 3)² + (y + 4)² = 10
Since the equations for standard form use r², we can rewrite the equation as:
10[(x - 3)² + (y + 4)²] = 100
Canceling the 10 on the left side, we get:
(x - 3)² + (y + 4)² = 10
Therefore, this equation represents a circle.
4. Equation: (x - 2)² + (y + 3)² = 49
This equation is already in standard form, so we can conclude that it represents a circle.
5. Circle with center at (1, -2) and passing through the origin:
Substituting the coordinates and solving for r:
(1 - 1)² + (-2 + 2)² = r²
0² + 0² = r²
Therefore, the radius is 0, and the equation of the circle is:
(x - 1)² + (y + 2)² = 0
6. Equation: x² + y² = 0
This equation represents a point-circle since the radius is zero.
7. Circle with center at (6, 0) and radius of 6:
Using the standard form equation:
(x - 6)² + (y - 0)² = 6²
(x - 6)² + y² = 36
8. Circle with center at (0, 0) and radius of 4:
Using the standard form equation:
(x - 0)² + (y - 0)² = 4²
x² + y² = 16