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The line\mathrm{4 x+3 y-4=0} divides the circumference of the circle centred at (5, 3), in the ratio 1: 2. Then the equation of the circle is

 

Option: 1

\mathrm{x^2+y^2-10 x-6 y-66=0}


Option: 2

\mathrm{x^2+y^2-10 x-6 y+100=0}


Option: 3

\mathrm{x^2+y^2-10 x-6 y+66=0}


Option: 4

 None of these.


Answers (1)

best_answer

Since \mathrm{4 x+3 y-4=0} is dividing the circumference in the ratio 1: 2, angle subtended at the centre = 2π/3.

Also the perpendicular distance from the centre to the given line is 5

⇒  Radius = 10

⇒  equation of  the  circle  is \mathrm{x^2+y^2-10 x-6 y-66=0 \text {. }}.

 

Posted by

Shailly goel

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