If the line 2x - y +1=0 touches the circle at the point (2,5) and the centre of the circle lies on the line x + y -9 =0. find the equation of the circle.
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1 Answers
21suppose the centre of the required circle is at h,k so we have h + k = 9
let us shift the origin to h,k
so the new equation of the tangent becomes 2X - Y + 2h - k +1 =0
now point of contact is given by - 2a2/c , a2 / c where c = 2h - k +1
after shifting of origin (2,5) becomes (2- h), (5- k)
so - 2a2/c = (2- h) and a2 / c = (5- k)
solving we get the values of h,k and a
equation of circle is (x- h)2 + ( y- k)2 = a2
