SOLUTION: Please help me solve this equations,write the equations of the following ellipse in their cannonical forms and hence, determine their Foci and vertices: 1) 4x^2+5y^2-24x-20y+36=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Please help me solve this equations,write the equations of the following ellipse in their cannonical forms and hence, determine their Foci and vertices: 1) 4x^2+5y^2-24x-20y+36=0       Log On


   

Question 411564: Please help me solve this equations,write the equations of the following ellipse in their cannonical forms and hence, determine their Foci and vertices:
1) 4x^2+5y^2-24x-20y+36=0
2) x^2+3y^2+2x-24y+46=0
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Ellipses:

1) 4x^2+5y^2-24x-20y+36=0

   4(x^2-6x) + 5(y^2-4y) +36 = 0   |completing squares

   4[(x-3)^2 -9] + 5[(y-2)^2 -4] + 36 = 0

   4(x-3)^2 -36 + 5(y-2)^2 -20 + 36 = 0

   4(x-3)^2 + 5(y-2)^2  = 20

  +%28x-3%29%5E2%2F5+%2B+%28y-2%29%5E2+%2F4+=+1+  

C(3,2) V(3,4)&V(3,0) and V(3+sqrt(5),2)&V(3-sqrt(5),2)

    sqrt(5-4)= 1    f(4,2) and f(2,2)  





2) x^2+3y^2+2x-24y+46=0            |completing squares

   (x+1)^2 -1 +3[(y-4)^2 -16] + 46 = 0

   (x+1)^2 +3(y-4)^2 -49 + 46 = 0

   %28x%2B1%29%5E2%2F3+%2B+%28y-4%29%5E2%2F1+=+1     

 C(-1,4) V(-1,5)&V(-1,3) and V(-1+sqrt(3),4)&V(-1-sqrt(3),4)

  sqrt(3-1)=sqrt(2)       f(-1 +sqrt(2),4) and f(-1-sqrt(2),4)