JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the parabolas \(y^2 = 4b\,(x -c)\) and \(y^2 = 8ax\) have a common normal, then which one of the following is a valid choice for the ordered triad \((a, b, c)\) ?
- A \(\left( {\frac{1}{2},2,3} \right)\)
- B \((1, 1, 3)\)
- C \(\left( {\frac{1}{2},2,0} \right)\)
- D \((1, 1, 0)\)
Answer & Solution
Correct Answer
(B) \((1, 1, 3)\)
Step-by-step Solution
Detailed explanation
Normal to there \(2\) curves are \(y = m\left( {x - c} \right) - 2bm - b{m^3}\) \(y = mx - 4am - 2a{m^3}\) If they how a common normal \(\left( {c + 2b} \right) - 4a = \left( {2a - b} \right){m^2}\) (\(m=0\) corresponds axis ) \( \Rightarrow {m^2} = \frac{c}{{2a - b}} - 2 < 0\)…
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