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A certain circle can be represented by the following equation. x^2 + y^2 - 2y - 99 = 0 a. What...

Question:

A certain circle can be represented by the following equation.

{eq}x^2 + y^2 - 2y - 99 = 0 {/eq}

a. What is the center of this circle? (_____, _____).

b. What is the radius of the circle? _____ units.

Center-Radius Form of a Circle:

In geometry, a closed rounded shape that has all points of the round path at a constant distance from a fixed point that is present on the same plane is called a circle and the constant distance between the fixed point and the round shape is called the radius of the circle.

The fixed point is called the center of the circle.

The center-radius form for a circle whose radius is {eq}r {/eq} is written as-

$$(x-h)^{2}+(y-k)^{2} = r^{2} $$

here {eq}(h,k) {/eq} are the coordinates of the center of the circle

This form of the equation of the circle is known as the standard equation of the circle.

If the equation of a circle is given in the question then we have to convert that equation into the center-radius form after that by comparing the given equation from the standard form, we can find the coordinates of the center and the radius of the circle.

Answer and Explanation: 1

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Given equation of the circle is-

$$x^{2}+y^{2}-2y-99 = 0 $$

Now convert the expressions of {eq}y {/eq} into the perfect square-

$$\begin{align} ...

See full answer below.


Learn more about this topic:

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How to Find the Equation of a Circle

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Chapter 30 / Lesson 9
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There are two commonly used forms of equations for a circle, in this lesson we'll take a few minutes to examine and understand both forms, and be able to convert from one to the other.


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