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Conics yourself
A circle is created by the perpendicular intersection of a plane and a cone.
A hyperbola is formed when a plane vertically intersects both parts of a double cone.
An ellipse is formed when a plane intersects a cone, but quite perpendicularly.
the parabola is formed when a plane intersects a cone at an almost vertical angle.
The Equation of a circle is : (x-h)^2 + (y-k)^2 = r^2
Because all of these equations are not functions we must isolate y and plug the positive and negative of the solution into the calculator to make the graphs
The Equation of an ellipse is : ((x-h)^2)/a + ((y-k)^2)/b = 1
The (h,k) coordinates equal the center of the circle or ellipse.
The (x,y) coordinates in the equation are equal to a point on either graph.
The "a" and "b" tell how the ellipse has been stretched
the basic equation for a parabola is : y = x^2
the first basic equation for a hyperbola is : ((x-h)^2)/(a^2) - ((y-k)^2)/(b^2) = 1
-x= up/down hyperbola -y= left/right hyperbola
To find the foci use a^2-b^2=c^2 with the equation.when c is found go out that many spaces from the center to find the foci.
The Directrix is y=-p when there's a vertical axis, x=-p when the axis is horizontal
The focus is (0,P) when there's a vertical axis, (P,0) when the axis is horizontal
You can find the radius of a circle when only given the center and point on the cicle, by using the distance formula.
the second basic equation for a hyperbola is : ((y-k)^2)/(b^2) - ((x-h)^2)/(a^2) = 1
