Circle

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.