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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

aradhya singh

9 Years agoGrade Select Grade

1 Answer

Vikas TU

9 Years ago

A circle touching x-axis at (3,0) can be represented by

(3-h)^2 + ( 0 – 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.

Radius is (1+1+2)^1/2

Hence the radius of given circle is 4.

(3-h)^2 + ( 0 – 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 – k )^2 = 16 ------------1

Length of its chord intercepted on y-axis is given by (k^2 – 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) ^ ½.

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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

aradhya singh

1 Answer

Vikas TU

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