JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Two parabolas with a common vertex and with axes along \(x-\) axis and \(y-\) axis, respectively, intersect each other in the first quadrant. if the length of the latus rectum of each parabola is \(3\) , then the equation of the common tangent to the two parabolas is?
- A \(3\, (x +y)+4 = 0\)
- B \(8\, (2x+y)+3 = 0\)
- C \(4\, (x+y)+3 = 0\)
- D \(x+ 2y+3 = 0\)
Answer & Solution
Correct Answer
(C) \(4\, (x+y)+3 = 0\)
Step-by-step Solution
Detailed explanation
As origin is the only common point to \(x\) - axis and \(y\) - axis, so, origin is the common vertex Let the equation of two of parabolas be \(y^{2}=4 a x\) and \(x^{2}=4 b y\) Now latus rectum of both parabolas \(=3\) \(\therefore 4 a=4 b=3\) \(\Rightarrow a=b=\frac{3}{4}\)…
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