Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If the equation of the locus of a point equidistant from the point $\left(a_1, b_1\right)$ and $\left(a_2, b_2\right)$ is $\left(a_1-b_2\right) x+\left(a_1-b_2\right) y+c=0$, then the value of 'c' is
MathematicsStraight LinesJEE MainJEE Main 2003
Options:
  • A
    $\sqrt{\mathrm{a}_1^2+\mathrm{b}_1^2-\mathrm{a}_2^2-\mathrm{b}_2^2}$
  • B
    $\frac{1}{2} a_2^2+b_2^2-a_1^2-b_1^2$
  • C
    $\mathrm{a}_1^2-\mathrm{a}_2^2+\mathrm{b}_1^2-\mathrm{b}_2^2$
  • D
    $\frac{1}{2}\left(a_1^2+a_2^2+b_1^2+b_2^2\right)$
Solution:
2816 Upvotes Verified Answer
The correct answer is:
$\frac{1}{2} a_2^2+b_2^2-a_1^2-b_1^2$
$\left(h-a_1\right)^2+\left(k-b_1\right)^2=\left(h-a_2\right)^2+\left(k-b_2\right)^2$
$\left(a_1-a_2\right) x+\left(b_1-b_2\right) y+\frac{1}{2}\left(a_2^2+b_2^2-a_1^2-b_1^2\right)=0$
$C=\frac{1}{2}\left(a_2^2+b_2^2-a_1^2-b_1^2\right)$

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.