JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the line \(y=m x+c\) is a common tangent to the hyperbola \(\frac{x^{2}}{100}-\frac{y^{2}}{64}=1\) and the circle \(x^{2}+y^{2}=36,\) then which one of the following is true?
- A \(5 m =4\)
- B \(4 c^{2}=369\)
- C \(c^{2}=369\)
- D \(8 m+5=0\)
Answer & Solution
Correct Answer
(B) \(4 c^{2}=369\)
Step-by-step Solution
Detailed explanation
\(y=m x+c\) is tangent to \(\frac{x^{2}}{100}-\frac{y^{2}}{64}=1\) and \(x^{2}+y^{2}=36\) \(c^{2}=100 m^{2}-64 l c^{2}=36\left(1+m^{2}\right)\) \(\Rightarrow 100 m ^{2}-64=36+36 m ^{2}\) \(m ^{2}=\frac{100}{64} \Rightarrow m =\pm \frac{10}{8}\)…
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