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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)`.
Equation of the line PR is

A

`x cos theta + y sin theta = sin theta + cos theta +1`

B

`x sin theta +y cos theta = cos theta + sin theta - 1`

C

`x sin theta +y cos theta = cos theta + sin theta +1`

D

`x tan theta +y = 1 +cot ((theta)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`m_(CQ) = cot theta`
`m_(PR) =- tan theta`
Equation of PR is
`y -(1+cos theta) =- tan theta (x-(1+sin theta))`
or `y +x theta =(1+cos theta) +tan theta (1+sin theta)`
`= (cos theta (1+cos theta) +sintheta (1+sin theta))/(cos theta)`
or `y +x tan theta = (1+cos theta +sin theta)/(cos theta)`
or `x sin theta +ycos theta = (cos theta + sin theta +1)`
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