BITSAT 2017 Slot 2 Solved Paper

Let (t,m) be the other end of the chord drawn from the point (p,q) on the circle
x2+y2=px+qy
Their mid-point is (

t+p

2

,

m+q

2

)
Since, mid-point lies on X -axis i.e. y=0
m+q=0 ..........(i)
Also, (t,m) lies on the circle.
∴t2+m2−pt−qm=0 ..........(ii)
From Eqs. (i) and (ii), we get t2−pt+2q2=0
Which is quadratic in t such that, Discriminant >0
⇒p2−8q2>0⇒p2>8q2