A circle touches the x-axis at (3,0) and its radius is twice the radius of circle x^2+y^2-2x-2y-2=0;find the equation of circle and the length of its chord intercepted on the y-axis?

1 Answer
Feb 10, 2018

We can find the radius of the given circle by rearranging it as #(x-a)^2 +(y-b)^2 =r^2# (where, #r# is the radius,and #(a,b)# is the centre)

So,given equation is, #x^2+y^2-2x-2y-2=0#

or, #(x-1)^2 +(y-1)^2 =4#

So,its radius is #2 units# hence, our circle of concern will have a radius of #2*2=4 units#

So,its centre will be at #(3,4)# (see the diagram)
graph{(x-3)^2 +(y-4)^2=16 [-20, 20, -10, 10]}

So,its equation will be #(x-3)^2 +(y-4)^2 = 16#

Now,put #X=0# in the above equation you will get,two values of #y# i.e #6.64# and #1.35#

So,the length of the cord intercepted by #Y# axis will be #(6.64-1.35)=5.29#