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KCET2013MathematicsCircle

The area of the circle having its centre at (3,4) and touching the line 5 x+12 y-11=0 is

Options

  1. A16 sq units
  2. B4 sq units
  3. C12 sq units
  4. D25 sq units

Correct answer

A. 16 sq units

Step-by-step solution

Given, centre of the circle is (3,4) . Here, P C= Length of perpendicular to the line 5 x+12 y-11=0 from the centre of the circle. aligned P C &= |5(3)+12(4)-11| 25+144 = |15+48-11| 169 &= | 52 13 |=4 aligned 5 x+12 y-11=0 Radius of circle =P C=4 Hence, required area of circle = (radius) ²= (4)²=16 sq units

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