The equation of the hyperbola whose directrix is x + 2y = 1, focu… - Vidyadip

MCQ

The equation of the hyperbola whose directrix is $x + 2y = 1$, focus $(2, 1)$ and eccentricity $2$ will be

✓
${x^2} - 16xy - 11{y^2} - 12x + 6y + 21 = 0$
B
$3{x^2} + 16xy + 15{y^2} - 4x - 14y - 1 = 0$
C
${x^2} + 16xy + 11{y^2} - 12x - 6y + 21 = 0$
D
None of these

✓

Answer

Correct option: A.

${x^2} - 16xy - 11{y^2} - 12x + 6y + 21 = 0$

a
(a) ${(x - 2)^2} + {(y - 1)^2} = 4\left[ {\frac{{{{(x + 2y - 1)}^2}}}{5}} \right]$

==> $5[{x^2} + {y^2} - 4x - 2y + 5]$

$ = 4[{x^2} + 4{y^2} + 1 + 4xy - 2x - 4y]$

==> ${x^2} - 11{y^2} - 16xy - 12x + 6y + 21 = 0$.

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