52.5k views
2 votes
A circle has its center at points (5,-7) and it passes through the point (-5,1). Complete the equation.

a) (x - 5)² + (y + 7)² = 121
b) (x + 5)² + (y - 1)² = 121
c) (x - 5)² + (y + 7)² = 169
d) (x + 5)² + (y - 1)² = 169

1 Answer

3 votes

Final answer:

The correct equation of the circle with center at (5,-7) and passing through (-5,1) is (x - 5)² + (y + 7)² = 169, after calculating the radius using the distance formula.

Step-by-step explanation:

The student has asked for the completion of the equation of a circle with a center at (5,-7) that passes through the point (-5,1). To find the correct equation, we need to determine the radius of the circle which can be calculated using the distance formula: √[(x2 - x1)² + (y2 - y1)²], where (x1, y1) is the center of the circle and (x2, y2) is a point on the circle.

Substituting the given points into the distance formula, we get the radius r as: √[(-5 - 5)² + (1 - (-7))²] = √[(-10)² + (8)²] = √[100 + 64] = √164 = 13.

Now we insert the center coordinates and the radius into the standard form of the circle equation: (x - h)² + (y - k)² = r², where h and k are the x and y coordinates of the center, respectively. The correct equation of the circle is therefore: (x - 5)² + (y + 7)² = 169.

User Simon Guo
by
8.4k 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