Anybody can help?
Find the center and the foci of the ellipse given by the equation -y^2+10y-4=9x^2+12x. At what points, if any, does this ellipse intersect the line
y= 2(x+10)?

Question

Anybody can help?
Find the center and the foci of the ellipse given by the equation -y^2+10y-4=9x^2+12x. At what points, if any, does this ellipse intersect the line
y= 2(x+10)?

anonymous · Answer

$$(x-h)^{2}/a ^{2} + (y-k)^{2}/b ^{2} =1$$
try to get equation  in these form

anonymous · Answer

I know this equation. But I cant get the answer at the end :(

dumbcow · Answer

use substitution
replace y with 2(x+10) in ellipse equation

anonymous · Answer

see.... @AliceMath99

This equation may be rewritten as:
9x2 + Y2+ 12X -10Y +4=0
to find the center we have
h= 12/2*9 = (2/3) = Coefficient of x divided by 2 times coefficient X2
k= 10/2=5 coefficient of Y divided by two times coefficient of Y2
The center is at ((2/3),5)
the foci are at:
a=√1=1
b= √9 =3
then the distance between the foci is 2c=2*√(b2-a2) = 4√2
Then the foci are located at:
((2/3), (5+4√2)) and ((2/3), (5-4√2))
Please do the math......
Hope it helps!!