AP EAMCET Engineering 21 Sep 2020 Shift 1 Paper

Equation of given parabola
y2=16ax
and the line y=4mxOn simplifying the equation of parabola and line the y -coordinate of point A is ‌

4a

m

∴ The area bounded by given curves
=

∫

0

‌

4a

m

(‌

y

4m

−‌

y2

16a

)dy=‌

a2

12

 (given)
⇒[‌

y2

8m

−‌

y3

48a

]0‌

4a

m

=‌

a2

12

⇒‌‌‌

16a2

8m3

−‌

64a3

48m3a

=‌

a2

12

⇒‌‌‌

2

m3

−‌

4

3m3

=‌

1

12

⇒‌‌‌

6−4

3m3

=‌

1

12

⇒‌‌m2=8⇒m=2