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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.$$P(3,2), C(4,2)$$

a) $(x-4)^{2}+(y-2)^{2}=1$b) $x^{2}+y^{2}-8 x-4 y+19=0$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 9

Circles

An Introduction to Geometry

Functions

Linear Functions

Polynomials

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in this problem, we're going to be finding the center radius form and the standard form of the equation of a circle. So we're given a point on the Circle P and the center of the Circle Sea. And so, since the center radius form depends on the center of the circle H comma K, and then the radius of the circle are it might be best to start with that one. So let me draw a rough graph of it. So we have the center see at about 4.4 comma two and they sent in the point p at about three homer, too. So we know that the radius of the circle be one. So let me just start writing out the center radius worm. It's going to be ex minus four whole squared, plus why minus two Whole squared is equal to the R squared, which is one squared. And so with that, we will expand it into the standard form. We'll get X squared minus eight X plus 16 plus y squared minus four way plus for is equal the one. And if we were to combine terms and put it back into the standard form you get X squared plus y squared minus eight x. Let me just read that. A little neater minus four. Why? Plus 19 since we moved that one over and some 16 and four. So we get 20 minus one is 19 is all equal to zero. So visited two importance of the circles. Let your cure was just use the center and the radius in order to find the first equation and then expanded into the 2nd 1

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