Precalculus

posted by .

"Sketch the ellipse. Find the coordinates of its vertices and foci.

34. x^2 + 25y^2 - 6x - 100y + 84 = 0
(Hint: Complete the squares in x and y. Begin by writing the equation in this form: (x^2 - 6x + ___) + 25(y^2 - 4y + ___) = -84.)"


==> I used the hint that came with the problem, but as I tried to solve the equation into the general form for an ellipse, I was getting negative denominators, which would make a and b contain imaginary numbers. Does anyone know how to solve this? Any help is greatly appreciated! :)

  • Precalculus -

    x^2 + 25y^2 - 6x - 100y + 84 = 0
    x^ - 6x + 9 + 25(y^2 - 4y + 4) = -84 + 9 + 100
    notice in the y expression, I added 4 to the inside, but that was multiplied by 25, so I had to add 100 on the right side.
    (x-3)^2 + 25(y-2)^2 = 25

    (x-3)^2/25 + (y-2)^2 = 1

    so a^2 = 25, and b^2 = 1

    take it from there

  • Precalculus -

    Ohhhhh!!!!! This totally makes sense. I forgot to multiply the 4 by 25 before bringing it over to the other side. Thanks so much!! :D

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-calculus-ck answers

    Identify the graph of the equation 4x^2-25y^2=100. Then write the equation of the translated graph for T(5,-2) in general form. Answer: hyperbola; 4(x-5)^2 -25(y+2)^2=100 2)Find the coordinates of the center, the foci, and the vertices, …
  2. 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) …
  3. 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 …
  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. AlgebraII

    Choose the equation that best represents an ellipse for the given foci and co-vertices. Foci (+/-3,0) Co vertices (0, +/-6)
  8. Math/Algebra

    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).
  9. precalc

    Find the standard form equation for each ellipse described. 1) Major vertices at (0, 3) and (0, -3), minor vertices at (2, 0) and (-2, 0) 2) Major vertices at (7, 0) and (-7, 0), foci at (5, 0) and (-5, 0) 3) Minor vertices at (-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