Explain circle with the help of conic sections.

Conics sections are planes, cut at varied angles from a cone. The shapes vary according to the angle at which it is cut from the cone.

Answer: According to conic sections, a circle is a locus of a point equidistant from a fixed point.

The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Explanation:

A conic section is a curve obtained by the intersection of the surface of a cone with a plane. Thus, by cutting and taking different slices(planes) at different angles to the edge of a cone, we can create a circle, an ellipse, a parabola, or a hyperbola.

The circle is a type of ellipse with its eccentricity as zero.

The ratio of a : b is the eccentricity.

Here, a is the perpendicular distance from the focus to a point on the curve, and b is the distance from the nearest directrix to the point.

In the case of a circle, directrix is the tangent, so b = 0.

With higher eccentricity, the conic is less curved.

The equation for a circle is, x² + y² = a² (as radius is a)

Therefore, according to conic sections, a circle is a locus of a point equidistant from a fixed point with equation  x² + y² = a² (as the radius is a).