PA ANSWER PO PLEASE!!

1. what is the center and radius of the circle defined by the equation (×–3)^2 (y–2)^2=25?

Example:
x2 + 2x + 1 + y2 + 6y + 9 = 16
x2 + 2x + 1 + y2 + 6y + 9 - 16 = 0
x2 + y2 + 2x + 6y + 1 +9 - 16 = 0
x2 + y2 + 2x + 6y-6= 0

evaluate the square of the quantity
transpose the constant term, 16
arrange the terms by its degree
combine like terms

2. What is the center and radius of the circle defined by the equation ( ×– 3^2 + (y–2^2= 25?

Example:
(x + 1)2 + (y + 3)2 = 42
express the radius into exponential form
Remember that the center-radius formula is
(x - h)2 + (y - k)=r?,
Therefore, the h= -1 and k=-3, then r=4
Center: -1, -3) and Radius: 4

3. write the standard form of the equation of a circle with center at (-4,-3) and is tangent to the ×- axis

Example:
(x -(-5))2 + (y - 6)2 = 52
(x + 5)2 + (y - 6)2 = 52
x? + 10x + 25 + y2 - 12y + 36 = 25
x2 + 10x + y2 – 12y + 25 + 36 - 25 = 0
x2 + y2 + 10x - 12y + 25 = 0


4.What is the center and radius of the circle whose equation is
x^2 + y^2 - 24x + 10y +160= 0 ?

Example:
x2 - 16x + y2 + 8y = -31
transpose the constant term, 31
(x2 - 16x) + (y2 + 8y) = -31
group them by its common variable
(x2 - 16x + 64) + (y2 + 8y +16)=-31+64 + 16
then use completing the square
(x - 8)2 + (y + 4)2 = 49
rewrite the perfect square trinomial into
square of binomial
(x - 8)2 + (y + 4)2 = 72
express the radius into exponential form
Center: (8,-4) and Radius: 7

5. Determine the equation for the circle in the given figure.

Example:
a. Determine the center and radius from the given.
Center is at (4, 5) and Radius is 6 units.
b. Substitute the value for (h, k) and r to the center-
radius formula.
(x-4)+ (y-5)2 = 62.

6. write the standard form of the equation of a circle with center at the origin and radius 5.

Example:
(×–h^2 + (y–k)^2 = r^2
(×–0^2 + (y–0)^2 = 9^2
×^2 + y^2 = 81

7. A cellular phone network uses towers to transmit calls. If the equation of the circular area
transmits by the tower is represented by
(x - 5)2 + (y - 1)2 = 22. Can you identify if you are
inside or outside of the circular area, if your coordinate location is (6,0)? How about if your
location is (8,2)?

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