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Question

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


A
23 sq. Units
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B
32 sq. Units
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C
6 sq. Units
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D
none of these
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Solution

The correct option is B 23 sq. Units

x2+y2=4,C=(0,0),r=2

Let y=mx+rm2+1 be a tangent

y=mx+2m2+1

This passes through (1,3)

3=m+2m2+1

(3m)2=4(m2+1)

m2+323m=4m2+4

3m2+23m+1=0

(m+13)2=0m=13

Equation is

y=x3+dfrac43

x+3y=4

Equation of normal will be

3xy+c=0

But normal passes through (1,3)

C = 0

3xy is equation of normal

Tangent, normal and x-axis form a triangle with vertices at (0,0) ,(4,0),(1,3)

Area=12×4×3=23


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