If P is a variable point and F 1 and F 2 are two fixed points such that |PF 1 – PF 2 | =…
Mathematics · JEE Advanced · NTA Exams — Co-ordinate Geometry
If P is a variable point and F1 and F2 are two fixed points such that |PF1 – PF2| = 2a. Then the locus of the point P is a hyperbola, with points F1 and F2 as the two focii (F1F2 > 2a). If \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) is a hyperbola, then its conjugate hyperbola is \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=-1 .\) Let P(x, y) is a variable point such that \(\left|\sqrt{(x-1)^{2}+(y-2)^{2}}-\sqrt{(x-5)^{2}+(y-5)^{2}}\right|=3 .\)
If the locus of the point P represents a hyperbola of eccentricity e, then the eccentricity e’ of the corresponding conjugate hyperbola is :
- \(\frac{5}{3}\)
- \(\frac{4}{3}\)
- \(\frac{5}{4}\)
- \(\frac{3}{\sqrt{7}}\)
Answer
(C) 5 4
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