I will do the 2nd one, they are all basically the same
9x^2 + y^2 - 18x - 6y + 9 = 0
9(x^2 - 2x + ....) - (y^2 - 6y + ...) = -9
9(x^2 - 2x + 1) + (y^2 - 6y + 9) = -9 + 9 + 9
9(x - 1)^2 + (y - 3)^2 = 9
(x - 1)^2 + (y - 3)^2 / 9 = 1
you have an ellipse with centre (1,3)
a^2 = 1 ----> a =1
b^2 = 9 -----> b = 3
vertices are (2, 3) and (0, 3)
minor axis points: (1, 6) and (1, 0)
graph the equation on
h ttps://www.desmos.com/calculator
to verify. Of course delete the space at the front of the URL
1.X^2 + y^2 +2x+6y=26
what is the center
what is the radius
2.9x^{2} +y^{2} -18x -6y+9=0
what is the center
what are the vertices?
name the two points on the minor axis
3. (x-2)^2/16 - (y-1)^2/4 =1
what are the vertices
please show calculations/steps pls i really need it
3 answers
x^2 + y^2 + 2x + 6y = 26
x^2+2x + y^2+6y = 26
x^2+2x+1 + y^2+6y+9 = 26+1+9
(x+1)^2 + (y+3)^2 = 36
center at (-1,-3)
radius = 6
9x^2 + y^2 -18x -6y + 9 = 0
9x^2-18x + y^2-6y = -9
9(x^2-2x+1) + y^2-6y+9 = -9+9(1)+9
9(x-1)^2 + (y-3)^2 = 9
(x-1)^2/1 + (y-3)^2/9 = 1
center at (1,3)
a=1, b=3
vertices at (1,3±3)
(x-2)^2/16 - (y-1)^2/4 =1
center at (2,1)
a=4, b=2
vertices at (2±4,1)
x^2+2x + y^2+6y = 26
x^2+2x+1 + y^2+6y+9 = 26+1+9
(x+1)^2 + (y+3)^2 = 36
center at (-1,-3)
radius = 6
9x^2 + y^2 -18x -6y + 9 = 0
9x^2-18x + y^2-6y = -9
9(x^2-2x+1) + y^2-6y+9 = -9+9(1)+9
9(x-1)^2 + (y-3)^2 = 9
(x-1)^2/1 + (y-3)^2/9 = 1
center at (1,3)
a=1, b=3
vertices at (1,3±3)
(x-2)^2/16 - (y-1)^2/4 =1
center at (2,1)
a=4, b=2
vertices at (2±4,1)
THANK YOU BOTH OF YOU
1 answer