Manipal Entrance Test 2014 Math Paper

Given equation of parabola is y2=4ax.
Let the co-ordinates of B are (at2,2at), then the slope of AB=

2

t

since, BC⊥AB
∴ Slope of BC=

−t

2

The equation of BC is
y−2=−

t

2

(x−at2 )
∵ This line meets the X-axis at point C.
So, put y = 0, we get
⇒ x=4a+at2
So, the distance CD=4a+at2−at2
=4a