TS EAMCET · Maths · Hyperbola
The number of common tangents that can be drawn to the curves \(\frac{x^2}{16}-\frac{y^2}{9}=1\) and \(x^2+y^2=16\) is
- A 0
- B 1
- C 3
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
Tangent to hyperbola: \(y = mx \pm \sqrt{16m^2 - 9}\) Tangent to circle: \(y = mx \pm 4\sqrt{1+m^2}\) For common tangent with slope \(m\): \(\sqrt{16m^2 - 9} = 4\sqrt{1+m^2}\) \(16m^2 - 9 = 16(1+m^2)\) \(16m^2 - 9 = 16 + 16m^2\) \(-9 = 16\), which is a contradiction. No common…
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