PreCal
posted by Cal .
Find the standard form of the equation of the ellipse. (Remember center is midpoint between either foci or vertices)
(1) 9x^2+4y^2+36x24y+36=0
(2) Vertices: (0,5)(0,5)
Passes through the point (4,2)
Centered at the origin

PreCal 
Reiny
for the first one, complete the square :
9x^2+4y^2+36x24y+36 = 0
9(x^2 + 4x + ____) + 4(y^2  6y + ____) = 36
9(x^2 + 4x + 4) + 4(y^2  6y + 9) = 36+36+36
9(x+2)^2 + 4(y3)^2 = 36
divide each term by 36
(x+2)^2/4 + (y3)^2/9 = 1
for 2. remember that from the vertices we know a = 5
standard form with centre at (0,0) is
x^2/a^2 + y^2/b^2 = 1
so we have
x^2/25 + y^2/b^2 = 1
but (4,2) lies on it, so
16/25 + 4/b^2 = 1
I will leave it up to you to solve for b^2, and plug that back into the above equation.
Respond to this Question
Similar Questions

Precalculus
For the ellipse with equation 5x^2+64y^2+30x+128y211=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) … 
Algebra 2
Choose the equation that best represents an ellipse for the given foci and covertices. 1. foci (+2, 0) covertices (0, +4) 2. foci (+3, 0) covertices (0,+6) 3. foci (0, +3) covertices (+5, 0) Choose the equation for the hyperbola … 
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) 
Math
Find the center, vertices, foci, and eccentricity of the ellipse. 9x^2 + 4y^2  36x + 8y + 31 = 0 My answer was: center=(2,1) v=(2,10)(2,10) f=(2,11)(2,11) e=11/3 Where did I make a mistake? 
Math
Find the center, vertices, foci, and eccentricity of the ellipse. 9x^2 + 4y^2  36x + 8y + 31 = 0 I know the center is (2,1) For the vertices I had (3,1)(1,1) and the foci (3.8,1)(.20,1) and e = 1.80 but I think these are wrong. 
Algebra IIPlease check my calculation
Find center, vertices, covertices and foci for the following; (x3(^2/49 + (y4)^2/4 = 1 Center would be (3,4) A=7 b=2 Vertices would be found this way: (h+a,k) (37,4) (3+7,4) Vertices = (4,4) (10,4) Covertices (h,k+b) (3,42) … 
pre cal
finding the standard form the center eccentricity vertices foci and minor axis endpoints of the equation 12x^2+4y^224x4y+1=0 
precal
complete the square to identify what type of conic you have, identify the key parts indicated and then graph conic. parabola: vertex,focus, directrix, focal diameter. ellipse: center,vertices, foci, eccentricity. hyperbola: center, … 
math
let equation of an ellipse be x^2+4y^2+6x8y+9=0 a. Find the standard form of the ellipse b. Find the center c. Find the vertices d. Find the foci e. Find the eccentricity 
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, …