JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the common tangent to the parabolas, \(y ^{2}=4 x\) and \(x ^{2}=4 y\) also touches the circle, \(x^{2}+y^{2}=c^{2},\) then \(c\) is equal to
- A \(\frac{1}{2}\)
- B \(\frac{1}{2 \sqrt{2}}\)
- C \(\frac{1}{\sqrt{2}}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\(y=m x+\frac{1}{m}\left(\operatorname{tangent} a t y^{2}=4 x\right)\) \(y=m x-m^{2}\left(\operatorname{tangent} a t x^{2}=4 y\right)\) \(\frac{1}{ m }=- m ^{2}\) (for common tangent) \(m ^{3}=-1\) \(m=-1\) \(y=-x-1\) \(x+y+1=0\) This line touches circle \(\therefore\) apply…
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