JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the vertices of a hyperbola be at \((-2, 0)\) and \((2, 0)\) and one of its foci be at \((-3, 0)\), then which one of the following points does not lie on this hyperbola?
- A \(\left( { - 6 , 2\sqrt {10} } \right)\)
- B \(\left( {2\sqrt 6 , 5} \right)\)
- C \(\left( { 4 , \sqrt {15} } \right)\)
- D \(\left( { 6 , 5\sqrt {2} } \right)\)
Answer & Solution
Correct Answer
(D) \(\left( { 6 , 5\sqrt {2} } \right)\)
Step-by-step Solution
Detailed explanation
equation of hyperbola is \(\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{{b^2}}} = 1\) and \(ae = 3\) We know that \({a^2}{e^2} = {a^2} + {b^2}\) \(9 = 4 + {b^2} \Rightarrow {b^2} = 5\) Hence equation of hyperbola is \(\frac{{{x^2}}}{4} - \frac{{{y^2}}}{5} = 1\,\) Hence…
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