If x c + y d =1 is a line through the intersection of x a + y b =1 and x ~b + y a =1 and…
Mathematics · JEE Advanced · NTA Exams — Co-ordinate Geometry
If \(\frac{x}{c}+\frac{y}{d}=1\) is a line through the intersection of \(\frac{x}{a}+\frac{y}{b}=1\) and \(\frac{\mathrm{x}}{\mathrm{~b}}+\frac{\mathrm{y}}{\mathrm{a}}=1\) and the lengths of the perpendiculars drawn from the origin to these lines are equal in lengths then :
- \(\frac{1}{\mathrm{a}^{2}}+\frac{1}{\mathrm{~b}^{2}}=\frac{1}{\mathrm{c}^{2}}+\frac{1}{\mathrm{~d}^{2}}\)
- \(\frac{1}{\mathrm{a}^{2}}-\frac{1}{\mathrm{~b}^{2}}=\frac{1}{\mathrm{c}^{2}}-\frac{1}{\mathrm{~d}^{2}}\)
- none
Answer
(A) 1 a ^ 2 + 1 ~b ^ 2 = 1 c ^ 2 + 1 ~d ^ 2, (C)
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