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  4. An ellipse having foci at (3,3) and (-4,4) and passing through the origin has eccentricity equal to

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Q. An ellipse having foci at $(3,3)$ and $(-4,4)$ and passing through the origin has eccentricity equal to

Conic Sections

Solution:

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$ PS _1+ PS _2=2 a$
$3 \sqrt{2}+4 \sqrt{2}=2 a $
$\therefore 2 a =7 \sqrt{2}$
$\text { Also } 2 ae = S _1 S _2=\sqrt{1+49}=5 \sqrt{2} $
$\therefore \frac{2 ae }{2 a }=\frac{5 \sqrt{2}}{7 \sqrt{2}}=\frac{5}{7}= e \Rightarrow( C )$