JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(L_1\) be the length of the common chord of the curves \(x^2 + y^2\, = 9\) and \(y^2\, = 8x\), and \(L_2\) be the length of the latus rectum of \(y^2\, = 8x\), then
- A \(L_1 > L_2\)
- B \(L_1\, = L_2\)
- C \(L_1 < L_2\)
- D \(\frac{{{L_1}}}{{{L_2}}} = \sqrt 2 \)
Answer & Solution
Correct Answer
(C) \(L_1 < L_2\)
Step-by-step Solution
Detailed explanation
We have \({x^2} + \left( {8x} \right) = 9\) \({x^2} + 9x + x + 9 = 0\) \(x\left( {x + 9} \right) - 1\left( {x + 9} \right) = 0\) \(\left( {x + 9} \right)\left( {x - 1} \right) = 0\) \(x = - 9,1\) for \(x = 1,y = \pm 2\sqrt {2x} = \pm 2\sqrt 2 \) \({L_1} = \) Length of \(AB\)…
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