Question

A circle is tangent to the x axis at x=5 and has one y intercept at y=3, determine the other y intercept and the equation of the circle

Answer 1

from the picture, you see the center is up "k" units from x-axis but that is also the radius of the circle
--> k = r
general equation for circle
\[(x-h)^{2} + (y-k)^{2} = r^{2}\]
also note that h=5 since the center is directly above point (5,0)
Now to solve for r , plug in other given point (0,3) for x,y
\[(0-5)^{2}+(3-r)^{2} = r^{2}\]
\[25 + (9-6r+r^{2}) = r^{2}\]
\[r = \frac{34}{6} = \frac{17}{3}\]
circle equation:
\[(x-5)^{2} + (y-17/3)^{2} = (17/3)^{2}\]

Answer 2

to find other y_intercept, plug in x=0 and solve for y