Question

If y = mx divides the area bounded by lines x = 0, y = 0,

x = 3/2 and the curves y = 1 + 4x – x² in two equal parts, then m is equal to -

• A. 13/8
• B. 13/4
• C. 13/6
• D. None of these

Answer 1

Answer: (C)

13/6

Answer 2

Equation of the given curve is (x –2)² = – (y – 5) which is a parabola given

area = =

=$\left[ x + 2 x ^ { 2 } - \frac { x ^ { 3 } } { 3 } \right] _ { 0 } ^ { 3 / 2 }$ = 3/2 + 9/2 –9/18 = 39/8 Also A¢ =

= $\frac { \mathrm { m } } { 2 } \left[ \mathrm { x } ^ { 2 } \right] _ { 0 } ^ { 3 / 2 }$ = $\frac { 9 } { 8 } \mathrm {~m}$

As given $\frac { 9 } { 8 } \mathrm {~m}$ = $\frac { 1 } { 2 }$ $\left( \frac { 39 } { 8 } \right)$ ̃ m = 13/6