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Conic Sections | Circle & Parabola | Chapter-11 | Class-XI

The sections of the double napped right circular cone with the plane are called conic sections. eg:- circle, ellipse, parabola and hyperbola etc. all are the examples of conic sections.

APPLICATIONS:- These curves have wide applications in the field of planetary motion, design of telescope, antenas, reflectors of flash light and automobile headlights. Vertex of the double napped cone separate the cone into two parts each part is called Nappes. α (alpha) is the angle made by the generator with the x-axis.

DIFFERENT TYPES OF CONIC SECTIONS:-

CIRCLE:-

When β(beta) = 90, then intersection of cone with plane is called circle. For circle the value of eccentricity = 0 or e = 0

PARABOLA:-

When α= β then intersection of plane and cone gives parabola. For Parabola the value of eccentricity = 1 or e = 1 ELLIPSE:-

When α < β < 90 then intersection of plane and cone gives an ellipse. For ellipse the value of eccentricity < 1 or e < 1 HYPERBOLA:-

When 0 < β < α then the intersection of plane and cone gives a hyperbola.

For Hyperbola the value of eccentricity > 1 or e > 1

CIRCLE:-

A circle is the set of all points in the plane which are at equidistant from the fixed point in the plane. Fixed point is called the centre of the circle, and fixed distance is called the radius of the circle.

EQUATION OF THE CIRCLE:- Let us suppose that a circle of radius O(h,k) and let P(x,y) is any arbitrary point on the circle so that |OP| is the radius of the circle

This is called the standard form of equation of circle.

Equation of the circle having centre (h, k) and radius = r is

When centre is at the origin then equation of the circle is

Equation of the form x^{2} + y^{2} + 2gx +
2fy + c = 0 is called the general equation of the circle.

Centre of the ciecle is (-g, -f) or

Radius of the ciecle is given by

Ifg^{2} + f^{2} – c > 0, then the radius of the circle is real and the circle is also real.

If g^{2} + f^{2} – c = 0, then the radius of the circle is real and the circle is called a point circle.

If g^{2} + f^{2} – c < 0, then the radius of the circle is imaginary and the circle is called is also an imaginary circle and it is not possible to draw an imaginary circle.

Special Features of General Equations of a Circle

It is quadratic in both x and y.

Coefficient of x^{2} = Coefficient of y^{2}

There is no term containing xy.

It contains three arbitrary constants g, f and c

PARABOLA

A parabola is the set of all points in a plane which are at equidistant from the fixed line and the fixed point. Para means "for" and bola means "throwing"

The fixed line is called the directrix and the fixed point is called the focus.

AXIS:- A line through the focus and perpendicular to the directrix is called the axis of the parabola.

VERTEX :- The point of intersection of the parabola with the axis is called the vertex of the parabola.

LATUS RECTUM:- Latus 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.

Art Integrated Project on Conic Section Class 11

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Maths Conic Section Part 1 Class 11 NCERT-cbse mathematics

E-LESSON PLANNING FOR MATHEMATICS TEACHER CLASS 10TH lesson plan for maths class X cbse, lesson plans for mathematics teachers, Method to write lesson plan for maths class 10, lesson plan for maths class X, lesson plan for mathematics grade X, lesson plan for maths teacher in B.Ed. RESOURCE CENTRE MATHEMATICS LESSON PLAN (Mathematics) : CLASS 10 th Techniques of Making E-Lesson Plan : Click Here Click Here For Essential Components of Making Lesson Plan Chapter 1 : Number System

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