AP EAMCET Engineering 2018 Apr 24 Shift 1 Paper

The intersection point of y2=32x and 2x2=27y
The coordinate of point P(18,24)
Equation of tangent through the point P(18,24) on the parabola y2=32x
y.24=16(x+18)
3y=2x+36
The slope m1=

2

3

The equation of tangent on 2x2=27y
2x.18=27

(y+24)

2

3y=8x−72
Slope m2=

8

3

Angle between the tangents is
tan‌θ=

m2−m1

1+m1m2

=

8 3 − 2 3

1+ 8 3 × 2 3

=

18

25

The required value
5√tan‌θ=5×√

18

25

=3√2