AP EAMCET · Maths · Straight Lines
If a line \(A B\) of length \(r\) moves so that \(A\) and \(B\) always lie respectively on \(X\)-axis and \(y=6 x\), then the locus of mid-point of \(A B\) is
- A \(y=12 x\)
- B \((x-y / 3)^2+y^2=\frac{r^2}{2}\)
- C \((x-y / 3)^2+y^2=\frac{r^2}{4}\)
- D \(y=6 x\)
Answer & Solution
Correct Answer
(C) \((x-y / 3)^2+y^2=\frac{r^2}{4}\)
Step-by-step Solution
Detailed explanation
Given, \(A\) lies on \(X\)-axis and \(B\) lies on \(y=6 x\) and \(A B=r\). \(C\) is the mid-point of \(A B\). Let \(A \equiv(a, 0), B \equiv(c, 6 c)\) and \(C \equiv(h, k)\). Now, \(h=\frac{a+c}{2}\) and \(\frac{0+6 c}{2}=k\)…
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