Search any question & find its solution
Question:
Answered & Verified by Expert
If the lines $2 x-3 y=5$ and $3 x-4 y=7$ are the diameters of a circle of area 154 square units, then obtain the equation of the circle.
Solution:
1334 Upvotes
Verified Answer
Given lines are $: 2 x-3 y-5=0$
$$
3 x-4 y-7=0
$$
on solving the two above equations $x=1 \& y=-1$
$\therefore \quad$ centre of circle is $(1,-1)$
$\because \quad$ Area of circle $=154$
$\Rightarrow \quad 154=\pi r^2$
$\Rightarrow r^2=(154)\left(\frac{7}{22}\right) \Rightarrow r^2=49$
$\Rightarrow r=7$
Equation of circle is $(x-1)^2+(y+1)^2=(7)^2$ $\Rightarrow x^2+y^2-2 x+2 y=47$
$$
3 x-4 y-7=0
$$
on solving the two above equations $x=1 \& y=-1$
$\therefore \quad$ centre of circle is $(1,-1)$
$\because \quad$ Area of circle $=154$
$\Rightarrow \quad 154=\pi r^2$
$\Rightarrow r^2=(154)\left(\frac{7}{22}\right) \Rightarrow r^2=49$
$\Rightarrow r=7$
Equation of circle is $(x-1)^2+(y+1)^2=(7)^2$ $\Rightarrow x^2+y^2-2 x+2 y=47$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.