Answer: (x - 4)² + (y - 7)² = 9
<u>Explanation:</u>
The equation of a circle is: (x - h)² + (y - k)² = r² where
- (h, k) is the center
- r is the radius
Given: (h, k) = (4, 7)
Find the intersection of the given equation and the perpendicular passing through (4, 7).
3x - 4y = -1
-4y = -3x - 1
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Use substitution to find the point of intersection:
Use the distance formula to find the distance from (4, 7) to (5.8, 4.6) = radius
Input h = 4, k = 7, and r = 3 into the circle equation:
(x - 4)² + (y - 7)² = 3²
(x - 4)² + (y - 7)² = 9
