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Question

Question: The distance of the middle point of the line joining the points \((a\sin\theta,0)\) and \((0,a\cos\t...

The distance of the middle point of the line joining the points (asinθ,0)(a\sin\theta,0) and (0,acosθ)(0,a\cos\theta) from the origin is.

A

a2\frac{a}{2}

B

12a(sinθ+cosθ)\frac{1}{2}a(\sin\theta + \cos\theta)

C

a(sinθ+cosθ)a(\sin\theta + \cos\theta)

D

aa

Answer

a2\frac{a}{2}

Explanation

Solution

Mid-point will be (asinθ2,acosθ2)\left( \frac { a \sin \theta } { 2 } , \frac { a \cos \theta } { 2 } \right) and distance

from origin will be (asinθ20)2+(acosθ20)2=a2\sqrt { \left( \frac { a \sin \theta } { 2 } - 0 \right) ^ { 2 } + \left( \frac { a \cos \theta } { 2 } - 0 \right) ^ { 2 } } = \frac { a } { 2 }.