Search any question & find its solution
Question:
Answered & Verified by Expert
The radical axis of the co-axial system of circles with limiting points \((1,2)\) and \((-2,1)\) is
Options:
Solution:
1830 Upvotes
Verified Answer
The correct answer is:
\(3 x+y=0\)
The radical axis of the co-axial system of circles with limiting points \(A(1,2)\) and \(B(-2,1)\) is the perpendicular bisector of line joining limiting points \(A\) and \(B\).
\(\because\) Mid-point of \(A\) and \(B\) is \(\left(-\frac{1}{2}, \frac{3}{2}\right)\) and slope of perpendicular to \(A B\) is -3
\(\therefore\) Equation of required radical axis is
\(\begin{aligned}
& y-\frac{3}{2}=-3\left(x+\frac{1}{2}\right) \\
\Rightarrow & y-\frac{3}{2}=-3 x-\frac{3}{2} \\
\Rightarrow & 3 x+y =0
\end{aligned}\)
Hence, option (d) is correct.
\(\because\) Mid-point of \(A\) and \(B\) is \(\left(-\frac{1}{2}, \frac{3}{2}\right)\) and slope of perpendicular to \(A B\) is -3
\(\therefore\) Equation of required radical axis is
\(\begin{aligned}
& y-\frac{3}{2}=-3\left(x+\frac{1}{2}\right) \\
\Rightarrow & y-\frac{3}{2}=-3 x-\frac{3}{2} \\
\Rightarrow & 3 x+y =0
\end{aligned}\)
Hence, option (d) is correct.
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.