circle R . D Sharma

suppose 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