JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the lines \(x -2y = 12\) is tangent to the ellipse \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) at the point \(\left( {3,\frac{-9}{2}} \right)\), then the length of the latus rectum of the ellipse is
- A \(12\sqrt 2\)
- B \(9\)
- C \(8\sqrt 3\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(9\)
Step-by-step Solution
Detailed explanation
Tangent at \(\left( {3,\frac{{ - 9}}{2}} \right)\) \(\frac{{3x}}{{{a^2}}} - \frac{{9y}}{{2{b^2}}} = 1\) Comparing with \(x - 2y = 12\) \(\frac{3}{{{a^2}}} - \frac{9}{{4{b^2}}} = \frac{1}{{12}}\) \( \Rightarrow a = 6\) and \(b = 3\sqrt 3 \) Length of latus rectum…
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