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Question

The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle x2+y2=4 at (1,3) is

A
23
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B
32
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C
6
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D
None of these
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Solution

The correct option is A 23
Let A (1, 3) and the triangle formed be OAB where O is origin.
B is the point of intersection of the tangent with the X axis.
The tangent of the circle x2+y2=a2 at (acosθ,asinθ) is xcosθ+ysinθ=a.
So the tangent at A (1,3) is 3y+x=4 which intersects x axis at B(4,0).
The area af the triangle OAB is 23 sq.units.

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