191k views
1 vote
1. Which is the equation of a circle with center (–2, 3) and radius r = 5?

(x + 2)² + (y – 3)² = 10
(x + 2)² + (y – 3)² = 25
(x – 2)² + (y + 3)² = 10
(x – 2)² + (y + 3)² = 25

2. A circle with center (–1, 2) passes through point (2, –2). Which is true?
The radius is sqrt 5.
The diameter is 10.
The equation is (x + 1)² + (y – 2)² = 10.
The circumference is 25.

4. Which is the equation of a circle with diameter with A(5, 4) and B(–1, –4)?
(x – 5)² + (y – 4)² = 10
(x + 5)² + (y + 4)² = 100
(x – 2)² + y² = 25
(x + 2)² + y² = 5

User Michalk
by
8.4k points

1 Answer

6 votes
1) the main formula of circle equation is (x - a)² + (y – b)²= R², (a, b) is the center and R is the radius. So we replace easily (a, b) by (–2, 3), and R=5 for finding the answer, it is (x +2 )² + (y – 3)²= 5²= 25
2) if a circle (x - a)² + (y – b)²= R² , ((a, b) is the center) passes with A(u, v), so we can write the equation as (u- a)² + (v – b)²= R², so we have
(2 + 1)² + (-2 -2)² = R², R²=9+16=25, which implies R=5, and the diameter is given by D=2*R=10, so the answer is The diameter is 10.
3) firstly, D=AB, let's calculate the length of AB,
AB= sqrt[(5+1)^2+(4+4)^2]=sqrt[36+64]=sqrt[100], so D=AB=10, but we know that D=R*2, so R=10/2=5, the equation of the circle must be as follow (x - a)² + (y – b)²= R², after changing the value of R, the equation is
(x – 2)² + y² = 25


User SayJeyHi
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories