Question

Find the equation of the circle with center at (-2, -3) and passing through the point (2,5).

284

likes1419 views

Gene

4.5

86 Answers

1. Identify the center of the circle (h, k) = (-2, -3) .

2. Use the distance formula to find the radius r :

r = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

where (x_1, y_1) = (2, 5) and (x_2, y_2) = (-2, -3) .

3. Calculate the radius:

r = \sqrt{(2 - (-2))^2 + (5 - (-3))^2}

r = \sqrt{(2 + 2)^2 + (5 + 3)^2}

r = \sqrt{4^2 + 8^2}

r = \sqrt{16 + 64}

r = \sqrt{80}

r = 4\sqrt{5}

4. Write the equation of the circle using the standard form:

(x - h)^2 + (y - k)^2 = r^2

where h = -2 , k = -3 , and r = 4\sqrt{5} :

(x + 2)^2 + (y + 3)^2 = (4\sqrt{5})^2

(x + 2)^2 + (y + 3)^2 = 80

[Answer] (x + 2)^2 + (y + 3)^2 = 80

2. Use the distance formula to find the radius

where

3. Calculate the radius:

4. Write the equation of the circle using the standard form:

where

[Answer]

Frequently asked questions (FAQs)

What is the third side length in a triangle with side lengths 5 cm, 9 cm, and 12 cm, following the rules for congruence of triangles?

+

What are the characteristics of an ellipse function with a major axis of 6 units and a minor axis of 4 units?

+

What is the value of sine when the opposite side is 5 units and the hypotenuse is 10 units?

+

New questions in Mathematics