Question

The ratio in which the area bounded by the curves y² = 2x and x² = 12y is divided by the line x = 3, is -

• A. 15 : 49
• B. 13 : 48
• C. 12 : 37
• D. None of these

Answer 1

Answer: (A)

15 : 49

Answer 2

Total area = $\frac { 16 \times 3 \times 3 } { 3 }$ A = 48

Area between x = 0 and x = 3

A₁ = $\int _ { 0 } ^ { 3 } \left( y _ { 2 } - y _ { 1 } \right) d x$= = $\frac { 45 } { 4 }$

A₂ = A – A₁ = 48 – $\frac { 45 } { 4 }$ = $\frac { 147 } { 4 }$ $\frac { \mathrm { A } _ { 1 } } { \mathrm {~A} _ { 2 } }$ = $\frac { \frac { 45 } { 4 } } { \frac { 147 } { 4 } }$ = 15 : 49