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

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

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1 Answers

Vikas TU
14149 Points
6 years ago
A circle touching x-axis at (3,0) can be represented by
(3-h)^2 + ( 0 โ€“ k )^2 = r^2
radius is twice the radius of the circle x^2+y^2-2x-2y-2=0
Hence find radius of new circle.
ย 
Radius is (1+1+2)^1/2
  • 2.
Hence the radius of given circle is 4.
ย 
  • (3-h)^2 + ( 0 โ€“ k )^2 = 4^2
Since no other condition is given to find the center of the circle.The equation of circle is
  • (x-h)^2 + ( y โ€“ k )^2 = 16ย  ------------1
Length of its chord intercepted on y-axis is given by (k^2 โ€“ c)^ 1/2 where equation of circle is in the form
x^2 + y^2 + 2hx + 2ky + c = 0 ----------------2
Comparing equations 1 and 2
Hence length of chord is (1- (r^2) ^ ยฝ.

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