If P and Q are points with eccentric angles θ and θ+(π)/6 on the ellipse (x^2)/16+(y^2)/4=1, then the area (in sq. units) of the triangle OPQ (where O…

Question

If P and Q are points with eccentric angles θ and θ+(π)/6 on the ellipse (x^2)/16+(y^2)/4=1, then the area (in sq. units) of the triangle OPQ (where O is the origin) is equal to

MARKS Content Team · Accepted Answer

Correct answer: 2. Let, P=4cos⁡θ,2sin⁡θ and Q=4cosθ+(π)/6,2sinθ+(π)/6 ⇒Area of ΔOPQ=1/2 4cos⁡θ 2sin⁡θ 1 4cosθ+(π)/6 2sinθ+(π)/6 1 0 0 1 =4cos⁡θsinθ+(π)/6-cosθ+(π)/6sin⁡θ =4sinθ+(π)/6-θ=4sin(π)/6=2 sq. units

If $P$ and $Q$ are points with eccentric angles $θ$ and $(θ + \frac{π}{6})$ on the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{4} = 1,$ then the area (in sq. units) of the triangle $O P Q$ (where $O$ is the origin) is equal to

Solution

More Ellipse Questions

If P and Q are points with eccentric angles θ and θ+π6 on the ellipse x216+y24=1, then the area (in sq. units) of the triangle OPQ (where O is the origin) is equal to

Solution

More Ellipse Questions

If $P$ and $Q$ are points with eccentric angles $θ$ and $(θ + \frac{π}{6})$ on the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{4} = 1,$ then the area (in sq. units) of the triangle $O P Q$ (where $O$ is the origin) is equal to