AP EAMCET · Maths · Straight Lines
On the locus of the point \(P(x, y)\) equidistant from \((3,0)\) and \((0,4)\). If \(A\) and \(B\) are two points that satisfy \(4 x=3 y\) and \(x=y\) respectively, then the distance between \(A\) and \(B\) is
- A \(\frac{5}{2}\)
- B \(5\)
- C \(\frac{25}{4}\)
- D \(25\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
\(P Q=P R\) \(\begin{aligned} & \Rightarrow \quad \sqrt{(x-3)^2+(y-0)^2}=\sqrt{(x-0)^2+(y-4)^2} \\ & \Rightarrow x^2-6 x+9+y^2=x^2+y^2-8 y+16 \\ & \Rightarrow 6 x-8 y+7=0 \\ & \Rightarrow y=\frac{6 x+7}{8}\end{aligned}\) Let \(A=\left(\alpha, \frac{6 \alpha+7}{8}\right)\) and…
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