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Question

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

A
32
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B
3
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C
23
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D
6
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Solution

The correct option is C 23
x2+y2=4
Differentiating wrt x, we get
dydx=xy,m=13
Equation of tangent: y3=13(x1)
3y3=x+1
x+3y=4

Area=∣ ∣y21(1+m2)2m∣ ∣=23

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