Explanation
This aspect of pure mathematics is conic sections. Conic sections are sections of a double cone (i.e. two equal circular cones placed with their vertices in contact and having the same axis) made by plane. These conics consist of the following curves: and the magnitude of the eccentricity (usually
(i) for a pair of intersecting straight lines. eccentricity \(e=\infty\)
(ii) for a circle \(e=0\)
general equation of a circle:
\(x^{2}+y^{2}+2 g x+2 f y+c=0\)
where \((-a,-g)\) is the centre of the circle
(iii) For a parabola \(e=1\)
simplest form of the equation of a parabola: \(v=4 a x\)
where \(a\) is the distance from the vertex of the parabola to the direction of \(x\)
(iv) for an ellipse \(e<1\) equation: \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\)
(v) for an hyperbola. \(e>1\)
equation: \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)