JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(3 x+4 y=12 \sqrt{2}\) is a tangent to the ellipse \(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{9}=1\) for some a \(\in \mathrm{R},\) then the distance between the foci of the ellipse is
- A \(4\)
- B \(2\sqrt 7\)
- C \(2\sqrt 5\)
- D \(2\sqrt 2\)
Answer & Solution
Correct Answer
(B) \(2\sqrt 7\)
Step-by-step Solution
Detailed explanation
\(3 \mathrm{x}+4 \mathrm{y}=12 \sqrt{12}\) is tangent to \(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{9}=1\) \(c^{2}=m^{2} a^{2}+b^{2}\) \(\Rightarrow a^{2}=16\) \(\mathrm{e}=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4}\) Distance between focii…
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