SOLUTION: I need your help The equation of a circle with radius is (x-h)^2+ (y-k)^2 if the center is at (h,k) Find the condition that a circle shall a. touch the x-axis b.have its center

Question 771657: I need your help
The equation of a circle with radius is (x-h)^2+ (y-k)^2 if the center is at (h,k) Find the condition that a circle shall
a. touch the x-axis
b.have its center on the y-axis
c.touch both axes
d.have its center on the line 3x+4y=12

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The equation of a circle with radius is if the center is at

Each of the conditions sets (fixes) something about , and , but one or two of those variables will still be free to take any value. The un-fixed variable(s) will still be in the equation, and the equation will represent an infinite number of circles.

a. If the circle touches the x-axis (is tangent to the x-axis), the center is at a distance from the x-axis, at point
so the equation is

b. If the circle has its center on the y-axis (which is the line , the center is at and the equation is

c. If the circle touches both axes, the center is at a distance from both axes, at point and the equation is

d. If the circle has its center on the line ,
then
--> --> -->
and the equation gets ugly:

RELATED QUESTIONS
Good day. Ineed your help.Thank you 2. The equation of a circle with radius is (x-h)^2+... (answered by josgarithmetic)

2. The equation of a circle with radius is (x-h)^2+ (y-k)^2 if the center is at (h,k)... (answered by Alan3354)

Find the center (h,k) of the circle with the equation x^2+y^2-6y=7. (h,k)=(_,_) a. 0,9 (answered by kiru_khandelwal)

I need help in finding what H, K , R. Also finding the center of the circle. Find... (answered by jsmallt9)

3x^2+3y^2−12x−12y−3=0 is the equation of a circle with center (h,k) and (answered by lwsshak3)

Xx+yy=x+2. I need to decide if it is an ellipse, parabola, hyperbola, or a circle. Once I (answered by lwsshak3)

Find the center (h,k) and radius of the circle with given equation... (answered by ewatrrr)

a circle has the equation x^2 = y^2=121. what is the center... (answered by ewatrrr)

with the equation: {{{2x^2-10x+2y^2-18y=1}}} how do I make an equation for a circle... (answered by Alan3354)