JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the line \(ax + y = c,\) touches both the curves \(x^2 + y^2 = 1\) and \(y^2 - 4\sqrt 2 x ,\) then \(|c|\) is equal to
- A \(\frac {1}{\sqrt 2}\)
- B \(\sqrt 2\)
- C \(\frac {1}{2}\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(\sqrt 2\)
Step-by-step Solution
Detailed explanation
Tangent to \({y^2} = 4\sqrt 2 x\) is \(y = mx + \frac{{\sqrt 2 }}{m}\) it is also tangent to \({x^2} + {y^2} = 1\) \( \Rightarrow \left| {\frac{{\sqrt 2 /m}}{{\sqrt {1 + {m^2}} }}} \right| = 1 \Rightarrow m = \pm 1\) \( \Rightarrow \) Tnagent will be \(y = x + \sqrt 2 \) or…
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