# NCERT Class 11-Math's: Exemplar Chapter –11 Conic Sections Part 2

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**11.1.3 Parabola**

A parabola is the set of points P whose distances from a fixed point F in the plane are equal to their distances from a fixed line *l* in the plane. The fixed point F is called focus and the fixed line *l* the directrix of the parabola.

Standard equations of parabola

The four possible forms of parabola are shown below in Fig. 11.7 (a) to (d). The lotus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the parabola (Fig. 11.7).

Main facts about the parabola

Forms of Parabolas | ||||

Axis | ||||

Directrix | ||||

Vertex | ||||

Focus | ||||

Length of lotus rectum | ||||

Equations of latus rectum |

Focal distance of a point

Let the equation of the parabola be and be a point on it. Then the distance of P from the focus is called the focal distance of the point, i.e.,

11.1.4 Ellipse

An ellipse is the set of points in a plane, the sum of whose distances from two fixed points is constant. Alternatively, an ellipse is the set of all points in the plane whose distances from a fixed point in the plane bears a constant ratio, less than, to their distance from a fixed line in the plane. The fixed point is called focus, the fixed line a directrix and the constant ratio (*e*) the centricity of the ellipse.

We have two standard forms of the ellipse, i.e.,

(i)

In both cases and .

In (i) major axis is along *x*-axis and minor along *y*-axis and in (ii) major axis is along and minor along *x*-axis as shown in Fig. 11.8 (a) and (b) respectively.

Main facts about the Ellipse:

Forms of the ellipse | ||

Equation of major axis | ||

Length of major axis | ||

Equation of Minor axis | ||

Length of Minor axis | ||

Directories | ||

Equation of latus rectum | ||

Length of latus rectum | ||

Centre |

Focal Distance:

The focal distance of a point on the ellipse is

from the nearer focus

from the farther focus

Differences of the focal distances of any point on a hyperbola is constant and equal to the length of the transverse axis.

Parametric equation of conics:

Conics | Parametric equation | |

(i) | Parabola | |

(ii) | Ellipse: | |

(iii) | Hyperbola: |