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

Question

An ellipse having foci at (3,3) and (-4,4) and passing through the origin has eccentricity equal to (A) (3/7) (B) (2/7) (C) (5/7) (D) (3/5)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5b5551f5108824d7c18c3a188e89bda2-.png" /> PS 1+ PS 2=2 a 3 √2+4 √2=2 a ∴ 2 a =7 √2 text Also 2 ae = S 1 S 2=√1+49=5 √2 ∴ (2 ae /2 a )=(5 √2/7 √2)=(5/7)= e ⇒( C )

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

$\frac{3}{7}$

$\frac{2}{7}$

$\frac{5}{7}$

$\frac{3}{5}$

$P S_{1} + P S_{2} = 2 a$
$32 + 42 = 2 a$
$∴ 2 a = 72$
$Also 2 a e = S_{1} S_{2} = 1 + 49 = 52$
$∴ \frac{2 a e}{2 a} = \frac{5 2}{7 2} = \frac{5}{7} = e \Rightarrow (C)$

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

73​

72​

75​

53​