COMEDK · Maths · 15. Hyperbola
Equation of a hyperbola having foci at \((0, \pm \sqrt{10})\) and passing through the point \((2,3)\) is
- A \(\dfrac{x^2}{5}+\dfrac{y^2}{5}=1\)
- B \(y^2-x^2=5\)
- C \(\dfrac{x^2}{5}-\dfrac{y^2}{5}=1\)
- D \(\dfrac{x^2}{\sqrt{5}}-\dfrac{y^2}{\sqrt{5}}=1\)
Answer & Solution
Correct Answer
(B) \(y^2-x^2=5\)
Step-by-step Solution
Detailed explanation
The foci of the hyperbola are at \((0, \pm \sqrt{10})\), which implies the hyperbola is vertical with its center at \((0,0)\). The equation is of the form \(\dfrac{y^2}{a^2} - \dfrac{x^2}{b^2} = 1\). The distance of the foci from the center is \(ae = \sqrt{10}\), so…
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