AP EAMCET · Maths · Straight Lines
Suppose a point \(\mathrm{P}\) moves so that \(\mathrm{BP}^2-\mathrm{AP}^2=121\), where \(A\) and \(B\) are \((2,5)\) and \((5,11)\) respectively. Then the locus of \(\mathrm{P}\) is a straight line, whose slope is
- A \(1 / 2\)
- B \(-2\)
- C \(-1 / 2\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(-1 / 2\)
Step-by-step Solution
Detailed explanation
Let \(\mathrm{P}(h, k)\) be the point \(B P^2-A P^2=121\) \(\begin{aligned} & (11-k)^2+(5-h)^2-(h-2)^2-(k-5)^2=121 \\ & 121+k^2-22 k+25+h^2-10 h-h^2-4+4 h \\ & -k^2-25+10 k=121\end{aligned}\)…
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