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JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A ray of light through \((2,1)\) is reflected at a point \(P\) on the \(y\) - axis and then passes through the point \((5,3)\). If this reflected ray is the directrix of an ellipse with eccentrieity \(\frac{1}{3}\) and the distance of the nearer focus from this directrix is \(\frac{8}{\sqrt{53}}\), then the equation of the other directrix can be :
- A \(2 x-7 y-39=0\) or \(2 x-7 y-7=0\)
- B \(11 x+7 y+8=0\) or \(11 x+7 y-15=0\)
- C \(2 x-7 y+29=0\) or \(2 x-7 y-7=0\)
- D \(11 x-7 y-8=0\) or \(11 x+7 y+15=0\)
Answer & Solution
Correct Answer
(C) \(2 x-7 y+29=0\) or \(2 x-7 y-7=0\)
Step-by-step Solution
Detailed explanation
Equation of reflected Ray \(y-1=\frac{2}{7}(x+2)\) \(7 y-7=2 x+4\) \(2 x-7 y+11=0\) Let the equation of other directrix is \(2 x-7 y+\lambda\) Distance of directrix from Focub \(\frac{a}{e}-a e=\frac{8}{\sqrt{53}}\)…
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