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STD 11 - 10.2 parabola,ellipse,hyperbola — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 10.2 parabola,ellipse,hyperbola4 Marks
MCQ
The equation of an ellipse whose focus $(-1, 1)$, whose directrix is $x - y + 3 = 0$ and whose eccentricity is $\frac{1}{2}$, is given by
  • ✓
    $7{x^2} + 2xy + 7{y^2} + 10x - 10y + 7 = 0$
  • B
    $7{x^2} - 2xy + 7{y^2} - 10x + 10y + 7 = 0$
  • C
    $7{x^2} - 2xy + 7{y^2} - 10x - 10y - 7 = 0$
  • D
    $7{x^2} - 2xy + 7{y^2} + 10x + 10y - 7 = 0$
✓

Answer

Correct option: A.
$7{x^2} + 2xy + 7{y^2} + 10x - 10y + 7 = 0$
a
(a) Let any point on it be $(x,y)$, then $\frac{{\sqrt {{{(x + 1)}^2}} + \sqrt {{{(y - 1)}^2}} }}{{\left| {\frac{{x - y + 3}}{{\sqrt 2 }}} \right|}} = \frac{1}{2}$

Squaring and simplifying, we get

$7{x^2} + 2xy + 7{y^2} + 10x - 10y + 7 = 0$.

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