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In $3-10$ , the coordinates of point $P$ on the circle with center at $C$ are given. Write an equation of each circle: a. in center-radius form b. in standard form.$$P(0,-3), C(0,0)$$

a) $x^{2}+y^{2}=9$b) $x^{2}+y^{2}-9=0$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 9

Circles

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Campbell University

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Lectures

01:32

In mathematics, the absolu…

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In $3-10$ , the coordinate…

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00:37

Write the standard equatio…

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(a) find the center-radius…

00:32

in this problem. We're ex divined wth e stand her radius and standard form of a circle, given the point on the circle and the central circle since we the two forms that given below the information. So the center radius form depends on the center, which was which is going to be on the form each comma K and the radius of the circle, which will be given by the point on the circle in relation to the center. Because we know that if the point lies in the circle, it'll be it is all points that lie on the circle or equal distance from the center. That's just one of the properties. So if we started with the circle centered, that's here. Ah, and we went out to the 0.0 comma minus three. We find that the radius is equal to three because that's how far we went down the Y axis. And so if we just continue onward, we'll find that Ah Thesent er radius Forum falls unders X minus zero cool squared, Plus why minus zero Whole squared is equal to three squared, so that will be X squared. Plus, y squared is equal to nine. And then if we wanted the standard form, we would leave the constant on the right over so we would get X squared. Plus y squared minus nine is equal is here. Let me just label the answers is a and this is B and those were the year two forms that we can write the equation of us are going.

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