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AP EAMCET20227 Jul 2022Evening ShiftMathematicsHyperbolaActual

If (1,2) is the focus, x+2 y=0 is the directrix and 2 is the eccentricity of a hyperbola, then the equation of the hyperbola is

Options

  1. Ax^2-y^2=a^2
  2. B3 x^2-8 x y-3 y^2-10 x-20 y+25=0
  3. Cx y=c^2
  4. D3 x^2-8 x y-3 y^2+10 x-20 y-25=0

Correct answer

B. 3 x^2-8 x y-3 y^2-10 x-20 y+25=0

Step-by-step solution

Focus is (1,2) , directrix is x+2 y=0, e= 2 Hyperbola is aligned & (x-1)^2+(y-2)^2=( 2 )^2 (x+2 y)^2 1+4 & x^2+1-2 x+y^2+4-4 y= 2 5 [x^2+4 y^2+4 x y ] & 5 x^2-10 x+5 y^2-20 y+25=2 x^2+8 y^2+8 x y & 3 x^2-8 x y-3 y^2-10 x-20 y+25=0 aligned

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