JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The line \(12 x \,\cos \theta+5 y \,\sin \theta=60\) is tangent to which of the following curves?
- A \(x^{2}+y^{2}=169\)
- B \(144 x^{2}+25 y^{2}=3600\)
- C \(25 x^{2}+12 y^{2}=3600\)
- D \(x^{2}+y^{2}=60\)
Answer & Solution
Correct Answer
(B) \(144 x^{2}+25 y^{2}=3600\)
Step-by-step Solution
Detailed explanation
\(12 x \cos \theta+5 y \sin \theta=60\) \(\frac{x \cos \theta}{5}+\frac{y \sin \theta}{12}=1\) is tangent to \(\frac{x^{2}}{25}+\frac{y^{2}}{144}=1\) \(144 \mathrm{x}^{2}+25 \mathrm{y}^{2}=3600\)
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