Right triangle ABC is located at A (−1, −2), B (−1, 1), and C (−5, 1) on a coordinate plane. What is the equation of a circle A with radius ?Group of answer choices(x + 1)2 + (y + 2)2 = 9(x + 5)2 + (y − 1)2 = 16(x + 1)2 + (y + 2)2 = 25(x + 5)2 + (y − 1)2 = 25
Question
Right triangle ABC is located at A (−1, −2), B (−1, 1), and C (−5, 1) on a coordinate plane. What is the equation of a circle A with radius ?Group of answer choices(x + 1)2 + (y + 2)2 = 9(x + 5)2 + (y − 1)2 = 16(x + 1)2 + (y + 2)2 = 25(x + 5)2 + (y − 1)2 = 25
Solution
The equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
From the given points, we can see that point A (-1, -2) is the center of the circle. The radius is not given, but we can calculate it using the distance formula between two points, which is √[(x₂ - x₁)² + (y₂ - y₁)²].
Let's calculate the distance between point A and point B to get the radius:
r = √[(-1 - (-1))² + (-2 - 1)²] = √[0 + 9] = 3
So, the equation of the circle is (x + 1)² + (y + 2)² = 3², which simplifies to (x + 1)² + (y + 2)² = 9.
Therefore, the correct answer is (x + 1)² + (y + 2)² = 9.
Similar Questions
What is the equation of a circle with center (-3, -5) and radius 4?A.(x - 3)2 + (y - 5)2 = 4B.(x - 3)2 + (y - 5)2 = 16C.(x + 3)2 + (y + 5)2 = 4D.(x + 3)2 + (y + 5)2 = 16SUBMITarrow_backPREVIOUS
This circle is centered at the point (4, 5), and the length of its radius is 3. What is the equation of the circle?A.(x + 4)2 + (y + 5)2 = 3B.(x - 5)2 + (y - 4)2 = 9C.(x - 4)2 + (y - 5)2 = 9D.(x2 - 4) + (y2 - 5) = 32SUBMITarrow_backPREVIOUS
Which circle does the point (-1, 1) lie on?(x-5)2 + (y+2)2 = 25(x-2)2 + (y+6)2 = 25(x-2)2 + (y-5)2 = 25(x-2)2 + (y-2)2 = 25
Find an equation of the circle that has center −6, 5 and passes through −2, 1.
Which of the following equations correctly represents a circle centered at the origin with a radius of 5?A.(x - 5)2 + y2 = 25B.(x - 5)2 + (y - 5)2 = 5C.x2 + y2 = 5D.x2 + y2 = 25SUBMITarrow_backPREVIOUS
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.