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In the diagram as shown, a circle is dra...


In the diagram as shown, a circle is drawn with centre `C(1,1)` and radius 1 and a line L. The line L is tangent to the circle at Q. Further L meets the y-axis at R and the x-axis at P in such a way that the angle OPQ equals `theta` where `0 lt theta lt (pi)/(2)`.
Area of triangle OPR when `theta = pi//4` is

A

`(1+ cos theta, 1 +sin theta)`

B

`(sin theta, cos theta)`

C

`(1+ sin theta, cos theta)`

D

`(1+sin theta, 1+ cos theta)`

Text Solution

Verified by Experts

The correct Answer is:
D

For the circle with center C, using parametric form at straight line, we get
`x - 1 = sin theta`
`y -1 = cos theta`
Thus, `Q -= (1+sintheta, 1 +cos theta)`
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