Given, line 2x+y−10=0 touches the circle at the point (3,4).
∵ Perpendicular to this line passes through centre of circle. Equation of line perpendicular to 2x+y−10=0 is ‌x−2y+λ=0 ⇒3−8+λ=0⇒λ=5 ∴‌x−2y+5=0 Centre of the circle be C(2k−5,k) Now radius r2=CP2=CQ2 r2=(2k−8)2+(k−4)2=(2k−6)2+(k+2)2 On solving this, we get k=2 ∵ Centre (−1,2) and radius =√20 Equation of circle be (x+1)2+(y−2)2=20 Clearly (−5,4) lies on the circle.