Algebra II

posted by .

Find the exact solution(s) of the system: (x^2/4)-y^2=1 and x=y^2+1

2)Write an equation for an ellipse if the endpoints of the major axis are at (-8,1) and (8,1) and the endpoints of the minor axis are at (0,-1) and (0,3).

Answer: (x^2/64) + (y-1)^2/4 = 1

Thanks a lot!!

• Algebra II -

(x^2/4)-y^2=1 and x=y^2+1

rewrite the second as y^2 = x-1 and sub into the first

x^2 /4 - (x-1) = 1
x^2 - 4x + 4 = 4 , I multiplied each term by 4
x(x-4) = 0
so x=0 or x=4

in y^2 = x-1
if x=0, y^2 = -1 ----> no solution
if x=4 , y^2 = 3 ---> y = ±√3

so they intersect at (4,√3) and (4,-√3)

2.
For the ellipse, the centre is (0,1), the midpoint of (-8,1) and (8,1)
(notice the (0,1) is also the midpoint of the minor axis)
a=8 and b=2, so....

(x^2)/64 + (y-1)^2 /4 = 1

Similar Questions

1. algebra

1)Write an equation for an ellipse if the endpoints of the major axis are at(1,6)and (1,-6)and the endpoints of the minor axis are at (5,0)and (-3,0) answer= (x-1)^2/36+y^2/16=1 2)Which is the equation of an ellipse with center (-4,2)and …
2. Algebra

Write an equation for an ellipse if the endpoints of the major axis are at (-8,1) and (8,1) and the endpoints of the minor axis are at (0,-1) and (0,3). d= sqrt(x2-x1)^2 +(y1-y2)^2 d= sqrt(8--8)^2 + (1-1)^2 d= sqrt 16 + 0 d= sqrt 256 …
3. Algebra

Find the exact solution(s) of the system: x^2/4-y^2=1 and x=y^2+1 A)(4,sqrt3),(4,-sqrt3),(-4,sqrt3),(-4,-sqrt3) B)(4,sqrt3),(-4,sqrt3) C)(2,1),(2,-1),(4,sqrt3),(4,-sqrt3) D)(4,sqrt3),(4,-sqrt3) I don't know
4. Math

Find the exact solution(s) of the system: x^2/4-y^2=1 and x=y^2+1 A)(4,sqrt3),(4,-sqrt3),(-4,sqrt3),(-4,-sqrt3) B)(4,sqrt3),(-4,sqrt3) C)(2,1),(2,-1),(4,sqrt3),(4,-sqrt3) D)(4,sqrt3),(4,-sqrt3)
5. Algebra II

Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0). My answer is y^2/36 + (x-1)^2/16 = 1. Is this correct?
6. Algebra II

Find the exact solution(s) of the system: (x^2/4)-y^2=1 and x=y^2+1 Answer:(4,sqrt3),(4,-sqrt3) 2)Write an equation for an ellipse if the endpoints of the major axis are at (-8,1) and (8,1) and the endpoints of the minor axis are at …
7. algebra

Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).
8. Algebra 2

I've got some homework about ellipses and I am not sure if I am doing these right. So if you could check my answers I would appreciate it. Thanks!! 1.) Write an equation for an ellipse if the endpoints of the major axis are at (1,6) …
9. Algebra 2

write an equation in standard form for the ellipse with endpoints of the major axis (-1,4) and (1,6)and endpoints of the major axisi at (-4,1) and (6,1) i have no idea how to start this
10. Pre Calculus

find an equation in standard form for the ellipse if the major axis endpoints are (-5,2) and (3,2); the minor axis length is 6.

More Similar Questions