AP EAMCET · Maths · Straight Lines
The locus of mid-points of points of intersection of \(x \cos \theta+y \sin \theta=1\) with the coordinate axes is
- A \(x^2+y^2=4\)
- B \(\frac{1}{x^2}+\frac{1}{y^2}= {4}\)
- C \(\frac{1}{x^2}+\frac{1}{y^2}=\frac{1}{2}\)
- D \(x^2+y^2=2\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{x^2}+\frac{1}{y^2}= {4}\)
Step-by-step Solution
Detailed explanation
Let the line cut the axes in \(A\) and \(B\) and if \((h, k)\) be the mid-point of \(A B\), then \(2 h=\frac{1}{\cos \theta}, 2 k=\frac{1}{\sin \theta}\) In order to find the locus, eleminate the variable \(\theta\) by \(\cos ^2 \theta+\sin ^2 \theta=1\)…
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