JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The locus of the point of intersection of the lines, \(\sqrt 2 x - y + 4\sqrt 2 k = 0\) and \(\sqrt 2 kx + ky - 4\sqrt 2 = 0\) ( \(k\) is any non-zero real parameter) is
- A A hyperbola with length of its transverse axis \(8\sqrt 2 \)
- B An ellipse with length ofits major axis \(8\sqrt 2 \)
- C An ellipse whose eccentricity is \(\frac{1}{{\sqrt 3 }}\)
- D A hyperbola whose eccentricity is \(\sqrt 3\)
Answer & Solution
Correct Answer
(A) A hyperbola with length of its transverse axis \(8\sqrt 2 \)
Step-by-step Solution
Detailed explanation
Here, lines are: \(\sqrt 2 x - y + 4\sqrt 2 k = 0\) \( \Rightarrow \sqrt 2 x + 4\sqrt 2 k = y\,\,\,.....\left( i \right)\) and \(\sqrt 2 kx + ky - 4\sqrt 2 = 0\,\,\,.....\left( {ii} \right)\) Put the value of \(y\) from \((i)\) in\((ii)\) we get :…
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