Q94 / 160 · AP EAMCET 2022 (08 Jul Shift 1) · Mathematics

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

  • A
    $(5,0)$
  • Correct answer
    B
    $(\sqrt{65}, 0)$
  • C
    $(7,0)$
  • D
    $(\sqrt{74}, 0)$

Solution

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

Hence, the correct answer is option: 'B'.

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