JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the tangent at a point on the ellipse \(\frac{{{x^2}}}{{27}} + \frac{{{y^2}}}{3} = 1\) meets the coordinate axes at \(A\) and \(B,\) and \(O\) is the origin, then the minimum area (in sq. units) of the triangle \(OAB\) is
- A \(3\sqrt 3\)
- B \(\frac {9}{2}\)
- C \(9\)
- D \(\frac {9}{\sqrt 3}\)
Answer & Solution
Correct Answer
(C) \(9\)
Step-by-step Solution
Detailed explanation
Equation of tangent to ellipse \(\frac{x}{{\sqrt {27} }}\cos \theta + \frac{y}{{\sqrt 3 }}\sin \theta = 1\) Area bounded by line and co-ordinate axis \(\Delta = \frac{1}{2}.\frac{{\sqrt {27} }}{{\cos \,\theta }}.\frac{{\sqrt 3 }}{{\sin \theta }} = \frac{9}{{\sin 2\theta }}\)…
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