Identify the conic equation ellipse parabola hyperbola Once

Identify the conic equation (ellipse, parabola, hyperbola). Once identified, do whatever is necessary (complete the square, etc.) to put that equation into the standard \"h-k\" form for that thing, in preparation for graphing it. y^2 - x + 3 = 0 x^2 + 2 y^2 - 6x + 4 y = 5 4x^2 - y^2 - 6y - 18 = 0 Which of the equations from Problem 4 was the ellipse? Write down here both the original equation and the final equation in standard form that you obtained in Problem 4. Fill in the steps for graphing it, and graph it! Identify h and k and give the coordinates of the center: Identify a and b: Give coordinates of vertices (on major axis): Give coordinates of \"not-vertices\" (on minor axis): Solve for c (c^2 = a^2 - b^2): Give coordinates of foci: Sketch the conic, clearly marking and labeling all the points (and lines) of interest:

Solution

a) y^2 -x +3 =0

y^2 = x-3

y^2 = (x-3)

Equation of parabola with vertex ( 3,0)

b) x^2 +2y^2 -6x +4y =5

x^2 -6x +2(y^2 +2y) =5

(x^2 -6x +9) -9 +2(y^2 +2y +1) -2 =5

(x-3)^2 +2(y+1)^2 = 16

(x-3)^2/16 + (y-1)^2/16

equation of ellipse with centre ( 3, 1)

c) 4x^2 -y^2 -6y -18 =0

4(x^2) - (y^2 +6y +9 -9) -18 =0

4x^2 - (y+3)^2 -9 =0

4x^2 -(y+3)^2 =9

x^2/ (9/4) - (y+3)^2/9 =1

Equation of hyperbola with centre( 0, -3)