Find a Parabola with Vertex (3,1) Focus (4,1)
Find the vertex of 4y^2+4y-16x+13=0
Find the center of an ellipse 9x^2+4y^2-36x-24y-36=0
Find an ellipse with minor axis of 8 and vertices at (-9,3),(7,3)
2 answers
answers please btw steps arent necessary
1. V(3 , 1), F(4 , 1).
X = a(Y - k)^2 + h,
VF = 1/4a = 4 - 3 = 1,
1/4a = 1,
4a = 1,
a = 1/4.
Eq: X = 1/4(Y - 1)^2 + 3.
2. 4Y^2 + 4Y - 16X +13 = 0.
-16X + 4Y^2 + 4Y = -13,
-4X + Y^2 + Y = -13/4,
-4X + Y^2 + Y + (1/2)^2 = -13/4 + 1/4.
-4X + ((Y + 1/2)^2 = -12/4 = -3,
-4X = -(Y + 1/2)^2 - 3,
X = 1/4(Y + 1/2)^2 + 3/4.
V(3/4 , -1/2).
X = a(Y - k)^2 + h,
VF = 1/4a = 4 - 3 = 1,
1/4a = 1,
4a = 1,
a = 1/4.
Eq: X = 1/4(Y - 1)^2 + 3.
2. 4Y^2 + 4Y - 16X +13 = 0.
-16X + 4Y^2 + 4Y = -13,
-4X + Y^2 + Y = -13/4,
-4X + Y^2 + Y + (1/2)^2 = -13/4 + 1/4.
-4X + ((Y + 1/2)^2 = -12/4 = -3,
-4X = -(Y + 1/2)^2 - 3,
X = 1/4(Y + 1/2)^2 + 3/4.
V(3/4 , -1/2).
2 answers