AP EAMCET · Maths · Hyperbola
Let \((1,2)\) be the focus and \(x+y+1=0\) be the directrix of a hyperbola \(\mathrm{H}\). If \(\sqrt{3}\) is the eccentricity of \(\mathrm{H}\), then its equation is
- A \(x^2-6 x y+y^2-14 x-22 y+17=0\)
- B \(x^2-6 x y+y^2+10 x+14 y-7=0\)
- C \(x^2+6 x y+y^2-14 x-22 y+17=0\)
- D \(x^2+6 x y+y^2+10 x+14 y-7=0\)
Answer & Solution
Correct Answer
(D) \(x^2+6 x y+y^2+10 x+14 y-7=0\)
Step-by-step Solution
Detailed explanation
Given equation of directrix is \(x+y+1=0\) and Focus is \((1,2)=5\) Let \(P(x, y)\) be any point on hyperbola \(\mathrm{H}\) Let \(\mathrm{PM}\) be the length of the perpendicular from \(\mathrm{P}\) to the directrix. then \(\frac{P S}{P M}=\sqrt{3} \Rightarrow P S^2=3 P M^2\)…
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