TS EAMCET · Maths · Straight Lines
A line \(\mathrm{L}\) has intercepts \(\mathrm{a}\) and \(\mathrm{b}\) on the coordinate axes. When the coordinate axes are rotated through an angle \(\alpha\) keeping the origin fixed, the same line \(\mathrm{L}\) has intercepts \(\mathrm{p}\) and \(q\) on the new axes. Then
- A \(a^2+b^2=p^2+q^2\)
- B \(a^2+p^2=b^2+q^2\)
- C \(\frac{1}{a^2}+\frac{1}{p^2}=\frac{1}{b^2}+\frac{1}{q^2}\)
- D \(\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{p^2}+\frac{1}{q^2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{p^2}+\frac{1}{q^2}\)
Step-by-step Solution
Detailed explanation
When axes are rotated through \(\alpha\), new co-ordinates \((x \cos \alpha-y \sin \alpha, x \sin \alpha+y \cos \alpha)\) Original equation of \(L: \frac{x}{a}+\frac{y}{b}=1\) With shifted coordinates,…
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