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.
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).