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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Hyperbola

JEE Main · Mathematics · Hyperbola

If one of the roots of the equation x^2-5 x-14=0 is the length of...

If one of the roots of the equation x2−5x−14=0x^2-5 x-14=0 is the length of the semi conjugate axis of the hyperbola x2a2−y2b2=1\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 and the square of the other root is the semi-transverse axis then the focus of the hyperbola that lies on the positive xx-axis is

Options

  1. A(5,0)(5,0)
  2. B(65,0)(\sqrt{65}, 0)
  3. C(7,0)(7,0)
  4. D(74,0)(\sqrt{74}, 0)

Correct answer

B. (65,0)(\sqrt{65}, 0)

Step-by-step solution

Given equation is x2−5x−14=0x^2-5 x-14=0 how roots are −2,7-2,7 Let b=7b=7 and a=4a=4 hence C=72+92=65C=\sqrt{7^2+9^2}=\sqrt{65} hence S=(65,0)S=(\sqrt{65}, 0)
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