Parabolas
Which direction does y^2 =-12x open?
left
what is the center and radius of (x-1)^2 + (y-2)^2 = 16?
C(1, 2), r=4
What is the center of (x^2)/4 + (y^2)/9 =1, and is it vertical or horizontal?
(0,0), vertical
What are the vertices of (y^2)/16 - (x^2)/25 = 1
(0, 4) or (0, -4)
Tell which conic section it is (circle, parabola, hyperbola, or ellipse) x^2 + 6x – y + 5 = 0.
parabola
Give the coordinates of the focus and the equation of the directrix for y^2=-12x.
(-3,0), x=3
State the center-radius equation of a circle with a center at (-2,5) and radius of sqrt(7).
(x+2)^2+(y-5)^2=7
Find the vertices and foci of the ellipse x²/16 + y²/7 = 1
Vertices: (4,0), (-4,0)
Foci: (3,0), (-3,0)
what is the center and vertices of [(y-3)^2]/4 - [(x+2)^2]/9 = 1
Center (-2, 3)
Vertices (-2, 1), (-2, 5)
Tell which conic section it is (circle, parabola, hyperbola, or ellipse) 4x^2 + y^2– 8x – 2y = –1.
ellipse
State the focus of y=-6(x+3)^2-4
F(-3, -97/24)
Convert this equation into standard form. State the center of the circle and the radius. x²+y²+2x-4y-9=0
(x+1)² + (y-2)²=14
center: (-1,2) radius: sqrt(14)
Put the ellipse in 3x²+5y^2-12x+30y+42=0 in standard form and state its center.
(x-2)²/5 + (y+3)²/3 =1
(2, -3)
Find the EXACT values of the vertices, foci, and eccentricity. Simplify all answers.
(x - 4)^2 - 4(y + 1)^2 = 64
vertices: (12, -1), (-4, -1)
foci: (4+/- 4sqrt(5),-1)
e=(sqrt(5))/2
What is the equation of the conic in standard form, centered at the origin with e = 5/3 and a vertex at (0, 4)?
y^2/16 - x^2/(256/9) = 1
or
y^2/16 - 9x^2/256 = 1
Give the equation of the parabola with vertex at (2,3) and focus at (5,3)
(y-3)^2=12(x-2)
Write the center-radius equation of a circle with a center at (-3, -6) and passes through the point (-4, 8).
(x+3)² + (y+6)² = 197
Write the rectangular equation for the curve with parametric equations and state its center:
x = -3 + cos(t), y = 4sin(t)
(x+3)^2 /1 +y^2 /16 = 1
Center (-3,0)
Write the equation of the hyperbola with center (-1,4), vertices (-1,-3) and (-1,11), and foci (-1,-5) and (-1,13).
(y-4)^2 /49 - (x+1)^2 /32 = 1
Give two sets of parametric equations for: y = 2(x - 3)^2 - 17
x = t, y = 2(t - 3)^2 - 17
x = t + 3, y = 2t^2 - 17
Give the equation of the parabola with focus at (-4,3) and directrix y=8.
(x+4)^2 = -10(y-11/2)
Write the center-radius form of a circle whose endpoints of its diameter are (-10,4) and (-6,-4).
(x+8)^2+y^2=20
Write the standard form for the ellipse with its vertices at (3,-7) and (3,3) and its minor axis length is 6.
(x-3)^2 /9 + (y+2)^2 /25 = 1
What is the equation for the hyperbola in standard form: 4x^2 - 25y^2 - 24x + 250y - 489 = 0?
(y - 5)^2/4 - (x - 3)^2/25 = 1
Solve the system:
4x^2 -x - y^2 + 6 =0
2x - y = 3
(3/11, -27/11)