The circle 𝑥^2 + 𝑦^2 − 4𝑥 − 16𝑦 + 𝑘 = 0 touches the x-axis. Find k and the coordinates of the point of contact. Find the coordinates of the centre and the radius of the circle.
+128475 x^2 + y^2 - 4x -16y + k = 0 complete the square on x and y, subtract k from both sides
x^2 -4x + 4 + y^2 - 16y + 64 = - k + 4 + 64
(x - 2)^2 + ( y - 8)^2 = 68 - k
The center = (2, 8)
The radius = 8 so r^2 = 64 so.....k = 4
Here's a graph : https://www.desmos.com/calculator/6ucox9q4dw
