5. Find the equation of the circle tangential to the line 3x-4y+1=0 and with
centre at (4,7).
20

 (x - 4)² + (y - 7)² = 9

Explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²    where

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

                   -->      

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

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the answer would be   dignified - apex