The equation of the circle is: ((x - 10)^2 + (y + 14)^2 = 9).
The equation of the circle is: ((x - h)^2 + (y - k)^2 = 9) where ((h, k)) are the coordinates of the center.
The equation of the circle with center (10, -14) and tangent to x = 13 can be found using the formula for the equation of a circle: ((x - h)^2 + (y - k)^2 = r^2), where ((h, k)) are the coordinates of the center and (r) is the radius. Since the circle is tangent to the vertical line x = 13, the radius is the distance from the center to the line, which is 3. Therefore, the equation of the circle is: ((x - 10)^2 + (y + 14)^2 = 9).
The equation of the circle with center lying in the first quadrant and tangent to x = 8, y = 3, and x = 14 can be found using the same formula. Since the circle is tangent to the vertical lines x = 8 and x = 14, and the horizontal line y = 3, the radius is the distance from the center to the closest of these lines, which is 3. Therefore, the equation of the circle is: ((x - h)^2 + (y - k)^2 = 9), where ((h, k)) are the coordinates of the center.
Write the equation of each circle.
1.) Center (10,-14)
tangent to x=13
2.) Center lies in the first quadrant
tangent to x=8, y=3 and x=14