JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(y=m x+4\) is a tangent to both the parabolas, \(\mathrm{y}^{2}=4 \mathrm{x}\) and \(\mathrm{x}^{2}=2 \mathrm{by},\) then \(\mathrm{b}\) is equal to
- A \(128\)
- B \(-64\)
- C \(-128\)
- D \(-32\)
Answer & Solution
Correct Answer
(C) \(-128\)
Step-by-step Solution
Detailed explanation
\(y=m x+4\) is tangent to \(y^{2}=4 x\) \(\Rightarrow \mathrm{m}=\frac{1}{4}\) \(y=\frac{1}{4} x+4\) is tangent to \(x^{2}=2 b y\) \(\Rightarrow x^{2}-\frac{b}{2} x-8 b=0\) \(\Rightarrow \mathrm{D}=0\) \(b^{2}+128 b=0\) \(\Rightarrow \mathrm{b}=-128,0\)…
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