JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The slope of the line touching both the parabolas \({y^2} = 4x\) and \({x^2} = - 32y\), is
- A \(\frac{1}{8}\)
- B \(\frac{2}{3}\)
- C \(\frac{1}{2}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(y^{2}=4 x\) \(\Longrightarrow a=1\) \(x^{2}=-32 y\) \(\Longrightarrow a=-8\) tangent to the parabola \(y^{2}=4 x\) is \(y=m x+\frac{a}{m}\) \(\Longrightarrow y=m x+\frac{1}{m}---(1)\) tangent to the parabola \(x^{2}=-32 y\) is \(y=m x+a m^{2}\)…
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