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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 5 · Set 1 · Q29
Find a relation between x and y such that P (x, y ) is equidistant from the points A(3, 5) and B(7, 1). Hence, write the coordinates of the points on…
Find a relation between $\displaystyle x$ and y such that $\displaystyle \mathrm{P}(x, \mathrm{y})$ is equidistant from the points A$\displaystyle (3, 5)$ and B$\displaystyle (7, 1)$. Hence, write the coordinates of the points on $\displaystyle x$-axis and y -axis which are equidistant from points A and B .
Marking-scheme solution
\[\begin{aligned}
& P A=P B \Rightarrow P A^{2}=P B^{2} \\
& (x-3)^{2}+(y-5)^{2}=(x-7)^{2}+(y-1)^{2} \\
& \Rightarrow x-y=2
\end{aligned}
\]
∴ Required point on \(\displaystyle x\)-axis is \(\displaystyle (2,0)\)
& required point on \(\displaystyle y\)-axis is $\displaystyle (0, -2)$
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