How do you find the equation of a circle with centre (5,4) and just touches the x-axis?

1 Answer
georgef
Jul 20, 2016

The equation of a circle with centre in #(a,b)# and radius #r# is #(x-a)^2+(y-b^2)=r^2#

Explanation:

We know that the centre is #(a,b)=(5,4)#, so we only need to find out the radius. But the circle 'just touches' the x-axis, so the distance of the centre to the x-axis is 4 (see the figure):

graph{(x-5)^2+(y-4)^2=16 [-5.79, 14.21, -1.16, 8.84]}

Then the radius is 4, and the equation is:

#(x-5)^2+(y-4)^2=16#

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