The equation of an ellipse whose focus (-1, 1 | vedclass

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Question

(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|}} =

Vedclass · Accepted Answer

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

Vedclass · Answer

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

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

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