Conic Sections Class 11

Conic Sections Class 11 – When a plane cuts the cone other than the vertex, we have the following situations:

(a) When \(\beta = 90^{0}\) , the section is a circle

(b) When \(\alpha < \beta < 90^{0}\), the section is an ellipse

(c) When \(\alpha = \beta\); the section is a parabola

(d) When \(0 \leq \beta < \alpha\); the section is a hyperbola

Where, β is the angle made by the plane with the vertical axis of the cone.

Circle: Set of points in a plane equidistant from a fixed point. A circle with radius r and centre (h, k) can be represented as \(\left ( x-h \right )^{2}+\left ( y-k \right )^{2}=r^{2}\)

Parabola: Set of points in a plane that are equidistant from a fixed line and point. A parabola with a > 0, focus at (a, 0), and directrix x = – a can be represented as \(y^{2}=4ax\)

In parabola \(y^{2}=4ax\), the length of latus rectum is given by 4a.

Ellipse: The sum of distances of set of points in a plane from two fixed points is constant. An ellipse with foci on the x-axis can be represented as: \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\)

In ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\), the length of the latus rectum is given by \(\frac{2b^{2}}{a}\).

Hyperbola: The difference of distances of set of points in a plane from two fixed points is constant. The hyperbola with foci on the x-axis can be represented as:

\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)

In a Hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\), the length of latus rectum is given by \(\frac{2b^{2}}{a}\)

Conic Sections Class 11 Examples

Conic Sections Class 11
Conic Sections Class 11
Conic Sections Class 11
Conic Sections Class 11
Conic Sections Class 11
Conic Sections Class 11


Practise This Question

Kushagra drew two lines, l and m parallel to each other. He drew another line n which is parallel to m. His friend Manish says that the line n will be parallel to line l as well. Is the statement by Manish correct?