JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The area (in \(sq. units\)) of the smaller of the two circles that touch the parabola, \(y^2 = 4x\) at the points \((1, 2)\) and the axis is
- A \(4\pi \left( {2 - \sqrt 2 } \right)\)
- B \(8\pi \left( {3 - 2\sqrt 2 } \right)\)
- C \(4\pi \left( {3 + \sqrt 2 } \right)\)
- D \(8\pi \left( {2 - \sqrt 2 } \right)\)
Answer & Solution
Correct Answer
(B) \(8\pi \left( {3 - 2\sqrt 2 } \right)\)
Step-by-step Solution
Detailed explanation
Equation of tangent to the parabola \({y^2} = 4x\,\,at\) \(\left( {1,2} \right)\,\,\) is \(2y = 4\left( {\frac{{x + 1}}{2}} \right)\) \( \Rightarrow y = x + 1\) Equation of normal \(y = - x + 3\) Let center be \(C\left( {3 - r,r} \right)\) Now \(P{C^2} = {r^2}\)…
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