WBJEE · Maths · Hyperbola
The equation of the common tangent with positive slope to the parabola \(y^{2}=8 \sqrt{3} x\) and the hyperbola \(4 x^{2}-y^{2}=4\) is
- A \(y=\sqrt{6} x+\sqrt{2}\)
- B \(y=\sqrt{6} x-\sqrt{2}\)
- C \(y=\sqrt{3} x+\sqrt{2}\)
- D \(y=\sqrt{3} x-\sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(y=\sqrt{6} x+\sqrt{2}\)
Step-by-step Solution
Detailed explanation
Equation of tangent in slope form of parabola \(y^{2}=8 \sqrt{3} x\) is \[ y=m x+c \] where, \(\quad c=\frac{a}{m}\) \(\therefore\) \(c=\frac{2 \sqrt{3}}{m}\) Also, tangent to the hyperbola \[ 4 x^{2}-y^{2}=4 \] or \(\frac{x^{2}}{1}-\frac{y^{2}}{4}=1\) is…
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