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Math Help - Equation of an ellipse

  1. #1
    Member MathBlaster47's Avatar
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    Equation of an ellipse

    Is my answer to this question correct?

    What is the equation of the ellipse with foci at (0,-4) and (0,4) ant the sum of its focal radii being 10?

    Answer:
    \frac{x}{25}+\frac{y}{9}=1

    I think I have it right, but it never hurts to make sure...
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  2. #2
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    Hello, MathBlaster47!

    Probably an oversight . . . you forgot the "squares".


    Is my answer to this question correct?

    What is the equation of the ellipse with foci at (0,-4) and (0,4)
    and the sum of its focal radii being 10?

    Answer: . \frac{x^{\color{red}2}}{25}+\frac{y^{{\color{red}2  }}}{9}\:=\:1

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  3. #3
    Member MathBlaster47's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, MathBlaster47!

    Probably an oversight . . . you forgot the "squares".

    Indeed....an oversight, along with the [Math] tags.....
    Must remember to type slower!
    But the bright side is that I'm correct!
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  4. #4
    Junior Member StonerPenguin's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    Indeed....an oversight, along with the [tex] tags.....
    Must remember to type slower!
    But the bright side is that I'm correct!
    Um, actually there's one little error;
    It's \frac{x^2}{9}+\frac{y^2}{25}=1 not \frac{x^2}{25}+\frac{y^2}{9}=1 because it's an ellipse streched along the y-axis. Look at page 420, they show two guidelines (in grey); the one on the left shows the guideline for an ellipse having center (0, 0), foci (0, -c) and (0, c). You followed the guideline for an ellipse having center (0, 0), foci (c, 0) and (c, 0).

    I'll show ya;
    "The ellipse having center (0, 0), foci (0, -c) and (0, c), and sum of focal radii 2a has the equation;
    .............. \frac{x^2}{b^2}+\frac{y^2}{a^2}=1
    where b^2 = a^2 - c^2 "

    So, to go back to the orginal question;
    What is the equation of the ellipse with foci at (0,-4) and (0,4) ant the sum of its focal radii being 10?

    So 10 = 2a, so a = 5 and c = 4. Now plug those values in b^2 = a^2 - c^2 ;
    5^2 - 4^2 = b^2
    25 - 16 = 9 so b = 3
    Since the foci are on the y-axis, the major axis is vertical, so use the appropriate formula;
    \frac{x^2}{b^2}+\frac{y^2}{a^2}=1 plug in the values;
    \frac{x^2}{3^2}+\frac{y^2}{5^2}=1
    \frac{x^2}{9}+\frac{y^2}{25}=1

    Sorry if this is a little lengthy, I just wanted to make sure for the both of us. I actually erased my answers and wrote yours when I saw that ours were different but then I double checked Hoorah~
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  5. #5
    Member MathBlaster47's Avatar
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    Quote Originally Posted by StonerPenguin View Post
    Um, actually there's one little error;
    It's \frac{x^2}{9}+\frac{y^2}{25}=1 not \frac{x^2}{25}+\frac{y^2}{9}=1 because it's an ellipse streched along the y-axis. Look at page 420, they show two guidelines (in grey); the one on the left shows the guideline for an ellipse having center (0, 0), foci (0, -c) and (0, c). You followed the guideline for an ellipse having center (0, 0), foci (c, 0) and (c, 0).

    I'll show ya;
    "The ellipse having center (0, 0), foci (0, -c) and (0, c), and sum of focal radii 2a has the equation;
    .............. \frac{x^2}{b^2}+\frac{y^2}{a^2}=1
    where b^2 = a^2 - c^2 "

    So, to go back to the orginal question;
    What is the equation of the ellipse with foci at (0,-4) and (0,4) ant the sum of its focal radii being 10?

    So 10 = 2a, so a = 5 and c = 4. Now plug those values in b^2 = a^2 - c^2 ;
    5^2 - 4^2 = b^2
    25 - 16 = 9 so b = 3
    Since the foci are on the y-axis, the major axis is vertical, so use the appropriate formula;
    \frac{x^2}{b^2}+\frac{y^2}{a^2}=1 plug in the values;
    \frac{x^2}{3^2}+\frac{y^2}{5^2}=1
    \frac{x^2}{9}+\frac{y^2}{25}=1

    Sorry if this is a little lengthy, I just wanted to make sure for the both of us. I actually erased my answers and wrote yours when I saw that ours were different but then I double checked Hoorah~
    No problem, better "a little lengthy" than too short, confusing and frustration inducing.
    That said, many thanks for helping out!
    As a lolcat might say....Helpin' yous doin it rite!
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