1) What are the coordinates of the center of the circle?
2) What is the length of the radius?
3) Identify the coordinates of the four radius points.
4) After knowing the center and the radius of the circle, write the
equation of the circle in the standard from.
5) Write the equation of the circle in general form.
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Answer:
1.The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.
2.The definition of radius of a circle is the length of the line segment from the center of a circle to a point on the circumference of the circle. So, the radius is half the length of the diameter.
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5.We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.
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Answer:
1. The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.
2. The definition of radius of a circle is the length of the line segment from the center of a circle to a point on the circumference of the circle. So, the radius is half the length of the diameter.
3. Circles in the Coordinate Plane
Recall that a circle is the set of all points in a plane that are the same distance from the center. This definition can be used to find an equation of a circle in the coordinate plane.
4. The standard form of a circle is given below: (x – h)2 + (y – k)2 = r2, where the center is located at (h, k) and r is the length of the radius. In this case, h will be –3, k will be 6, and r will be 5. The answer is (x + 3)2 + (y – 6)2 = 25.
5. We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.
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