Once you have the transformation formula, invert it and substitute into the circle equation. You will find that the result is an ellipse. Indeed, the image of a circle under any affine transformation is some sort of ellipse. Knowing this, you can take a somewhat simpler approach.
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type.
Covering the system of circles, parabolas, ellipses, hyperbolas, the transformation of coordinates (change of axes), the general equation of conics, and the polar equations of conics (the...
A circle is formed at the intersection of the cone and the plane if the plane is at right angles to the vertical axis of the cone (i.e. parallel to the cone's base).
How to graph a circle in standard form and general form; for Algebra 2 students to learn about circleconicsections, with videos, examples and step-by-step solutions.
There are several possible ways to define the plane curves known as conicsections. No matter how they are introduced, other descriptions wil be useful in various circumstances.
Conicsection formulas represent the standard forms of a circle, parabola, ellipse, hyperbola. For ellipses and hyperbolas, the standard form has the x-axis as the principal axis and the origin (0,0) as the center.
The circle is the simplest and best known conicsection. As a conicsection, the circle is the intersection of a plane perpendicular to the cone's axis. The geometric definition of a circle is the locus of all points a constant distance from a point and forming the circumference (C).
The document discusses different conicsections and graph transformations. It defines circles, ellipses, parabolas, and hyperbolas as the shapes that result from cutting a cone with different planes.