# data[].attributes.body
parabola: Ax ² + Dx + Ey = 0
circle: x ² + y ² + Dx + Ey + F = 0
ellipse: Ax ² + Cy ² + Dx + Ey + F = 0
hyperbola: Ax ² – Cy ² + Dx + Ey + F = 0

# data[].attributes.body
x² + y² = r2 -Circle
x² / a² + y² / b² = 1 -Ellipse
4px = y2 -parabola
x² / a² - y² / b² = 1-Hyperbola

# data[].attributes.body
General Equation: Ax2+Bxy+Cy2+Dx+Ey+F=0

Circle: (x−h)2+(y−k)2=r2

Ellipse:
Hyperbola: (x−h)2a2−(y−k)2b2=1

(x−h)2a2−(y−k)2b2=1

Parabola

# data[].attributes.body
4 variables, theta, x, y, z,

# data[].attributes.body
Circle- When x and y are both squared and the coefficients on them are the same — including the sign.

Parabola- When either x or y is squared — not both.

Ellipse- When x and y are both squared and the coefficients are positive but different.

Hyperbola- When x and y are both squared, and exactly one of the coefficients is negative and exactly one of the coefficients is positive.

# data[].attributes.body
Conics have a general equation of Ax2+Bxy+Cy2+Dx+Ey+F=0

but each type also has an equation

# data[].attributes.body
General Equation for a conic section :

Ax² + Bxy + Cy² + Dx + Ey + F = 0

(If B² - 4AC is...)
< 0 = Ellipse, Circle, point, or no curve
= 0 = Parabola, 2 Parallel lines, 1 line or no curve
> 0 = Hyperbola or 2 intersecting lines

Circle: All of the variables are squared in the equation.
Ellipse: Both squared numbers and are adding together.
Hyperbola: Both squared number and are subtracting each other.
Parabola: The P in the equation 4Px = y^2 is the distance from the vertex to focus

# data[].attributes.body
(h,k) = center
Circle: (x-h)^2 + (y-h)^2 (no denominators), will equal the radius squared
Ellipse: (x-h)^2/a^2 + (y-h)^2/b^2, will always be equal to 1
Hyperbola: always equal to one, same as ellipse equation but the plus sign is switched to a minus
Parabola: (y-k)=a(x-h)^2

# data[].attributes.body
circle: x and y are both squared and are the same number
parabola: either x or y is squared but not both
ellipse: both are squared and positive but different numbers
hyperbola: ones positive and ones negative with different coefficients and both are squared

# data[].attributes.body
When the angle is 0, it makes a circle. When both the angle and Z are zero, it makes a degenerate ellipse. When the angle is 45, it makes a parabola. If Y and Z are 0, it makes a degenerate parabola.