How do you write the equation for a circle with center at (0, 0) and touching the line 3x+4y=10?
To find the equation of a circle we should have the center and radius.
Equation of circle is:
Where (a,b) : are the coordinates of the center and
r :Is the radius
Given the center (0,0)
We should find the radius .
Radius is the perpendicular distance between (0,0) and the line 3x+4y=10
Applying the property of the distance
# d = |A*m+B*n+C| / sqrt(A^2+B^2)#
The radius which is the distance from straight line
A=3. B=4 and C=-10
So the equation of the circle of center(0,0) and radius 2 is :