Math/Algebra

posted by .

Find the standard equation of an ellipse with the given characteristics and sketch the graph.
Vertices at (0,-5), and (0,5); Foci at (0,-4)and (0,4).

  • Math/Algebra -

    The ellipse is centred at the origin (0,0).

    The standard formula for the ellipse is then
    x²/a²+y²/b²=1
    where
    2a=distance between vertices on the major axis
    =(5-(-5)=10, so
    a=5

    Distance between foci
    2c=(4-(-4))=8
    so
    c=4

    To find b, we use the relation
    a²=b²+c²
    or
    5²=b²+4²
    b=sqrt(25-16)=3

    So the equation for the given ellipse is
    x²/5²+y²/3²=1

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-calculus

    For the ellipse with equation 5x^2+64y^2+30x+128y-211=0, find the cooridinates of the center, foci, and vertices. Then, graph the equation. my answer is: coordinates of center: (-3,1) foci:(-11,-1) and (4.7,-1) vertices: (-11,-1) (5,-1) …
  2. Algebra 2

    Choose the equation that best represents an ellipse for the given foci and co-vertices. 1. foci (+-2, 0) co-vertices (0, +-4) 2. foci (+-3, 0) co-vertices (0,+-6) 3. foci (0, +-3) co-vertices (+-5, 0) Choose the equation for the hyperbola …
  3. College Algebra.

    Find the equation in standard form of the ellipse, given Center (-2,4),vertices (-6,4) and(2,4) foci (-5,4) and (1,4)
  4. Math

    Find the vertices, center, asymptotes, and foci of the ellipse and sketch its graph: 9x^2-4y^2-18x+8y+41=0
  5. algebra

    Choose the equation that best represents an ellipse for the given foci and co-vertices. foci (+or- 3,0) co-vertices (o, + or- 6)
  6. algebra 2

    Graph the equation. Identify the vertices, co-vertices, and foci of the ellipse. 64x^2+16y^2=1024 This is what i have so far vertices (0,8)(0,-8) foci(0,4√3),(0,-4√3)
  7. Math

    Write the standard equation of the ellipse with the given characteristics Center:(0,0) foci: (2,0) (-2,0) vertices:(5,0) (-5,0)
  8. math please help me

    Write the standard equation of the ellipse with the given characteristics I have no ideal how to do this Center:(0,0) foci: (2,0) (-2,0) vertices:(5,0) (-5,0)
  9. Math

    Write the standard equation of the ellipse with the given characteristics Vertices: (0,7) (0,-7) foci: (0,2) (0,-2)
  10. mathematics

    Find the coordinates of foci, vertices, eccentricity of an ellipse and sketch the graph of equation:(x-2)^2\4+(y+3)^2\9=1

More Similar Questions