AP EAMCET · Maths · Hyperbola
The equation of the hyperbola with focus \((1,2), e=\sqrt{3}\) and directrix \(2 x+y=1\) is given by
- A \(2 y^2-12 x y-7 x^2+2 x-14 y+22=0\)
- B \(2 y^2+12 x y+7 x^2-2 x+14 y-22=0\)
- C \(2 y^2-12 x y-7 x^2-2 x-14 y-22=0\)
- D \(2 y^2+12 x y+7 x^2+2 x+14 y+22=0\)
Answer & Solution
Correct Answer
(A) \(2 y^2-12 x y-7 x^2+2 x-14 y+22=0\)
Step-by-step Solution
Detailed explanation
Given, Focus \((S)=(1,2)\) Eccentricity \((e)=\sqrt{3}\) Equation of Directrix is \(2 x+y=1\) Required equation of hyperbola is \(S P=e \mathrm{PM}\) \[ \sqrt{(x-1)^2+(y-2)^2}=\sqrt{3} \frac{|2 x+y-1|}{\sqrt{2^2+1^2}} \] Squaring on both sides,…
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