AP EAMCET · Maths · Hyperbola
The values of \(m\) for which the line \(y=m x+2\) becomes a tangent to the hyperbola \(4 x^2-9 y^2=36\) is
- A \(\pm \frac{2}{3}\)
- B \(\pm \frac{2 \sqrt{2}}{3}\)
- C \(\pm \frac{8}{9}\)
- D \(\pm \frac{4 \sqrt{2}}{3}\)
Answer & Solution
Correct Answer
(B) \(\pm \frac{2 \sqrt{2}}{3}\)
Step-by-step Solution
Detailed explanation
We have, line, \(y=m x+2\)... (i) Hyperbola, \(4 x^2-9 y^2=36... (ii)\) On solving eqs. (i) and (ii), we get \(x^2\left(4-9 m^2\right)-36 m x-72=0\) Since, this line is a tangent of hyperbola…
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