AP EAMCET Engineering 20 Apr 2019 Shift 2 Paper

Consider the equation of parabola
y2=9x
The equation of normal chord at a point t on the parabola is
tx+y=2(

9

4

)t+

9

4

t3
The chord subtends right angle at vertex of parabola V(0,0)
Thus
y2−9x(

tx+y

9 2 t+ 9 4 t3

)=0
The sum of the coefficient of x2 and y2 terms should be zero. Hence,
1−

9t

9 2 t+ 9 4 t3

‌‌=0
1−

1

1 2 + t2 4

‌‌=0

1

2

+

t2

4

‌‌=1
t2‌‌=2
Therefore, t=±√2