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Consider a family of circles which are passing through the point (−1, 1) and are tangent to xaxis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval (1) 0

Consider a family of circles which are passing through the point (−1, 1) and are tangent to xaxis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval (1) 0

Grade:12

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
ATQ the circle has centre =(h,k)
as it touches x axis,its radius is k, so its eqn would be:
(x-h)^2+(y-k)^2=k^2
(-1,1)=>(-1-h)^2+(1-k)^2=k^2
so h^2+2h-2k+2=0
here discriminant is greater than or equal to 0 for real values of h
so, 2k-1>=0
k>=1/2
so the set of values of k is given by interval [1/2,infinity)
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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