JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(5x + 9 = 0\) is the directrix of the hyperbola \(16x^2 -9y^2 = 144,\) then its corresponding focus is
- A \((5, 0)\)
- B \(\left( {\frac{5}{3},0} \right)\)
- C \((-5, 0)\)
- D \(\left( { - \frac{5}{3},0} \right)\)
Answer & Solution
Correct Answer
(C) \((-5, 0)\)
Step-by-step Solution
Detailed explanation
\(\frac{{{x^2}}}{9} - \frac{{{y^2}}}{{16}} = 1\) \(a = 3,b = 4\) and \(e = \sqrt {1 + \frac{{16}}{9}} = \frac{5}{3}\) corresponding focus will be \(\left( { - ae,0} \right)\) i.e. \(\left( { - 5,0} \right)\).
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