Circle 3 Question 3

3. The tangent and the normal lines at the point (3,1) to the circle x2+y2=4 and the X-axis form a triangle. The area of this triangle (in square units) is

(a) 13

(b) 43

(c) 23

(d) 13

(2019 Main, 8 April II)

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Answer:

Correct Answer: 3. (c)

Solution:

  1. Let T=0 and N=0 represents the tangent and normal lines at the point P(3,1) to the circle x2+y2=4.

So, equation of tangent (T=0) is

3x+y=4

For point A, put y=0, we get

x=43

Area of required OPA=12(OA)(PM)

=12×43×1[PM=y-coordinate of P]=23 sq unit 



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