WBJEE · Maths · Hyperbola
For the variable \(t,\) the locus of the points of intersection of lines \(x-2 y=t\) and \(x+2 y=\frac{1}{t}\) is
- A the straight line \(x=y\)
- B the circle with centre at the origin and radius 1
- C the ellipse with centre at the origin and one focus \(\left(\frac{2}{\sqrt{5}}, 0\right)\)
- D the hyperbola with centre at the origin and one focus \(\left(\frac{\sqrt{5}}{2}, 0\right)\)
Answer & Solution
Correct Answer
(D) the hyperbola with centre at the origin and one focus \(\left(\frac{\sqrt{5}}{2}, 0\right)\)
Step-by-step Solution
Detailed explanation
Given equation of lines are \[ x-2 y=t \] and \(\quad x+2 y=\frac{1}{t}\) On multiplying Eqs. (i) and (ii) we get \[ \begin{array}{r} (x-2 y)(x+2 y)=t \times \frac{1}{t} \\ \Rightarrow \quad x^{2}-4 y^{2}=1 \end{array} \]…
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