AP EAMCET · Maths · Hyperbola
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 \((5,0)\)
- B \((\sqrt{65}, 0)\)
- C \((7,0)\)
- D \((\sqrt{74}, 0)\)
Answer & Solution
Correct Answer
(B) \((\sqrt{65}, 0)\)
Step-by-step Solution
Detailed explanation
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 \(S=(\sqrt{65}, 0)\)
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