ok so here are 8 conic sections and an equation to get them. i needto know 6 thi
ID: 3090372 • Letter: O
Question
ok so here are 8 conic sections and an equation to get them. i needto know 6 thing about each conic section... and if some one wouldanswer it would be a life saver =]*parabola...
*the vertex
*axis of symmetry equation
*coordinates of the focus
*directrix equation
* length of the latus rectum
*ellipse...
*center
*length of major and minor axis of symmetry
*verticies
*foci
*Direction of the major axis (horizontal or vertical)
*hyperbola...
*Center
* length of transverse axis
* length of conjugate axis
* verticies
*Foci
* slopes of the asymptotes
x²-4x+4= -y²-2y+ 35
Ellipse
8y=x²-2x+25
Parabola
4x²+25y²-24-50y+61=100
Ellipse
x²=36-4y²
Ellipse
9x²-16y²+36x+32y=124
Hyperbola
-4y=x²-4x
Parabola
x²-14x+4=9y²-36y
Hyperbola
y²-3x+6y+12=0 Parabola
x²-4x+4= -y²-2y+ 35
Ellipse
8y=x²-2x+25
Parabola
4x²+25y²-24-50y+61=100
Ellipse
x²=36-4y²
Ellipse
9x²-16y²+36x+32y=124
Hyperbola
-4y=x²-4x
Parabola
x²-14x+4=9y²-36y
Hyperbola
y²-3x+6y+12=0 Parabola
Explanation / Answer
x²-4x+4= -y²-2y+ 35 Ellipse this is a circle: coefficients of the squaredterms are =; complete the square for each If you get completing the square, the rest should more easily fallinto place x^2 - 4x +4 + y^2 +2y = 35 (x-2)^2 + y^2 + 2y + ____ = 35 + ____ if we add 1 to both sides, the square is perfect (to find thenumber, take 1/2 * 2 (the coefficient of y) and square it) (1/2 * 2)^2 = 1 (x-2)^2 + y^2 + 2y + _1___ = 35 + __1__ (x-2)^2 + (y+1)^2 = 36 a^2 + b^2 = r^2 basic equation of a circle with center atorigin. center is (2, -1); r = 6, find the x- and y-intercepts. 8y=x²-2x+25 Parabola 8y + 1= (x^2 + 2x + _1___) +25 y = (1/8)(x +1)^2 +24/8 y = (1/8)(x + 1 )^2 + 3 this parabola opens up; vertex is at (-1, 3) the shape is a very fat parabola (the 1/8 coefficient tellsthat) 4x²+25y²-24-50y+61=100 [is there supposed tobe an x after -24??? -24x?? this is an ellipse because the 4x^2 and 25y^2; the 4 and 25 areboth the same sign and not equal (if equal, a circle) I thinkyou have a typo and am going forward with that assumption 4x^2 - 24x + 25y^2 - 50y = 100 - 61 4(x^2 - 6x + ____) + 25(y^2 -2y + ____) = 39 4(x^2 - 6x + __9___)+ 25(y^2 -2y + __1__) = 39 + 4(9) + 25(1) 4(x-3)^2 + 25(y-1)^2 = 100 4(x-3)^2 + 25(y-1)^2 = 100 100 100 100 (x-3)^2 + (y - 1)^2 = 1 25 4 center at (3, 1) major axis parallel to x-axis minor axis parallel to y-axis grab your book and look at examples for focal length, coordinatesof foci, this problem with the corrected typo (my assumption) makes muchmore sense for a book problem. use the examples and match the steps;
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