Final answer:
The equation of circle c with a center at (1,5) and that passes through point a (-4,3) is found by calculating the radius using the distance formula, and subsequently using the general equation of a circle. The result is (x - 1)² + (y - 5)² = 29.
Step-by-step explanation:
To find the equation of circle c with a center at (1,5) that passes through point a (-4,3), we need to calculate the radius of the circle first. The radius is the distance from the center of the circle to any point on the circle. Using the distance formula, we can find the radius r as follows:
- r² = (x2 - x1)² + (y2 - y1)²
- r² = (-4 - 1)² + (3 - 5)²
- r² = (-5)² + (-2)²
- r² = 25 + 4
- r² = 29
Now that we have the value of r², we can write down the equation of the circle using the general form (x - h)² + (y - k)² = r² where (h,k) is the center of the circle and r is the radius. Substituting the center (1,5) and r² = 29, the equation of the circle is:
(x - 1)² + (y - 5)² = 29.