If the lines $2 x-3 y=5$ and $3 x-4 y=7$ are the diameters of a circle of area 154 sq units, then equation…

If the lines $2 x-3 y=5$ and $3 x-4 y=7$ are the diameters of a circle of area 154 sq units, then equation of the circle is $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
  1. $x^2+y^2-2 x+2 y-47=0$
  2. $x^2+y^2-2 x+2 y-49=0$
  3. $x^2+y^2-2 x-2 y-47=0$
  4. $x^2+y^2-2 x-2 y-49=0$

Solution

Centre is point of intersection of $2 x-3 y=5$ and $3 x-4 y=7$ $i \cdot e \cdot(1,-1)$ and radius $r$ is such that $\pi r^2=154 \Rightarrow r=7$ Hence, the required equation is $\begin{aligned} & (x-1)^2+(y+1)^2=7^2 \\ \Rightarrow & x^2+y^2-2 x+2 y-47=0\end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 1)

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