It Can Be Shown That an Ellipse with Foci $( c , 0 )$

question 98

Short Answer

It can be shown that an ellipse with foci $( c , 0 )$ and $( - c , 0 )$ where the sum of the distances from any point ( $x , y )$ of the ellipse to the two foci is $2 a$ has equation $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { a ^ { 2 } - c ^ { 2 } } = 1$ . Use this result to find an equation of an ellipse with foci $( 3,0 )$ and $( - 3,0 )$ , where the sum of the distances from any point of the ellipse to the two foci is 10 .
A) $\frac { x ^ { 2 } } { - 3 } + \frac { y ^ { 2 } } { 100 } = 1$
B) $\frac { x ^ { 2 } } { - 3 } + \frac { y ^ { 2 } } { 22 } = 1$
C) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$
D) $x ^ { 2 } + y ^ { 2 } = 100$

• A) \(\frac { x ^ { 2 } } { - 3 } + \frac { y ^ { 2 } } { 100 } = 1\)
• B) \(\frac { x ^ { 2 } } { - 3 } + \frac { y ^ { 2 } } { 22 } = 1\)
• C) \(\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1\)
• D) \(x ^ { 2 } + y ^ { 2 } = 100\)

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