Question 972473
1.write an equation in standard form for the ellipse shown with center (0,0) , focus (0,6) co-vertex(0,-10).Given ellipse has a vertical major axis. (Note: focus and co-vertices cannot both be on the vertical major axis. I will assume you meant the co-vertex coordinates given are instead those of the vertex.)

Its standard form of equation: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, a>b, (h,k)=coordinates of center
center:(0,0)
a=10
a^2=100
c=6
c^2=36
c^2=a^2-b^2
b^2=a^2-c^2=100-36=64
equation: {{{x^2/100+y^2/64=1}}}

2. The area of a rectangle is equal to x^2 +7x +10 square units. if the length of the rectangle is equal to x+5 units, what expression represents its width? 
{{{(x^2+7x+10)/(x+5)}}}
{{{(x+5)(x+2)/(x+5)=(x+2)}}}
What expression represents its width? (x+2)