JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(m\) is the slope of a common tangent to the curves \(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\) and \(x^{2}+y^{2}=12\), then \(12\; m ^{2}\) is equal to
- A \(6\)
- B \(9\)
- C \(10\)
- D \(12\)
Answer & Solution
Correct Answer
(B) \(9\)
Step-by-step Solution
Detailed explanation
\(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\) equation of tangent to the ellipse is \(y=m x \pm \sqrt{a^{2} m^{2}+b^{2}}\) \(y=m x \pm \sqrt{16\; m^{2}+9}\) \(x^{2}+y^{2}=12\) equation of tangent to the circle is \(y=m x \pm \sqrt{12} \sqrt{1+m^{2}}\) for common tangent equate eq.…
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