WBJEE · Maths · Straight Lines
A variable line passes through a fixed point \(\left(x_{1}, y_{1}\right)\) and meets the axes at \(A\) and \(B\). If the rectangle \(O A P B\) be completed, the locus of \(P\) is, \((O\) being the origin of the system of axes).
- A \(\left(y-y_{1}\right)^{2}=4\left(x-x_{1}\right)\)
- B \(\frac{x_{1}}{x}+\frac{y_{1}}{y}=1\)
- C \(x^{2}+y^{2}=x_{1}^{2}+y_{1}^{2}\)
- D \(\frac{x^{2}}{2 x_{1}^{2}}+\frac{y^{2}}{y_{1}^{2}}=1\)
Answer & Solution
Correct Answer
(B) \(\frac{x_{1}}{x}+\frac{y_{1}}{y}=1\)
Step-by-step Solution
Detailed explanation
Let the equation of line be \(\frac{x}{a}+\frac{y}{b}=1\) since, the line passing through a fixed point \(\left(x_{1}, y_{1}\right)\). \(\therefore \quad \frac{x_{1}}{a}+\frac{y_{1}}{b}=1\) since, \(O A P B\) is a rectangle, therefore the coordinate of \(P\) will be \((a, b)\)…
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