If the lines $2 x+3 y+1=0$ and $3 x-y-4=0$ lie along diameters of a circle of circumference $10 \pi$, then…

If the lines $2 x+3 y+1=0$ and $3 x-y-4=0$ lie along diameters of a circle of circumference $10 \pi$, then the equation of the circle is
  1. $x^2+y^2-2 x+2 y-23=0$
  2. $x^2+y^2-2 x-2 y-23=0$
  3. $x^2+y^2+2 x+2 y-23=0$
  4. $x^2+y^2+2 x-2 y-23=0$

Solution

Intersection of given lines is the centre of the circle i.e. $(1,-1)$ Circumference $=10 \pi \Rightarrow$ radius $r=5$ $\Rightarrow$ equation of circle is $x^2+y^2-2 x+2 y-23=0$

Asked in: JEE Main 2004

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