Conic Sections — Class 11 Mathematics

Core Concepts

The circle, parabola, ellipse and hyperbola are conic sections. Their equations encode geometric properties such as distance from a centre, focus or directrix.

Worked Examples

The circle x²+y²−6x+4y−3=0 becomes (x−3)²+(y+2)²=16. Centre=(3,−2), radius=4.

For y²=4ax, the vertex is (0,0), focus is (a,0) and directrix is x=−a.

Explained MCQs

1. The radius of x²+y²=25 is 5.
2. The centre of (x−2)²+(y+3)²=9 is (2,−3).
3. For y²=4ax, the focus is (a,0).

Practice

1. Find the centre and radius of x²+y²+4x−8y−5=0.
2. Write the equation of a circle with centre (−2,3) and radius 5.