Conic Sections — Class 11 Mathematics
Mathematics · Chapter 10
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Chapter summary
Conic sections are the curves obtained when a plane cuts a double-napped right circular cone: a circle, ellipse, parabola or hyperbola according to the angle of the cut, with degenerate cases (a point, a line, a pair of lines) when the plane passes through the vertex. A circle is the set of points at fixed distance (radius) from a centre, with equation
Sections of a coneCircle and its equationParabola, focus, directrix and latus rectumEllipse, foci, eccentricity and latus rectumHyperbola, foci, eccentricity and latus rectumStandard equations and applications
Key ideas & terms
- Conic section
- A curve formed by intersecting a plane with a double-napped right circular cone.
- Circle
- Set of points at a fixed distance
from a centre; . - Parabola
- Set of points equidistant from a focus and a directrix; standard
. - Ellipse
- Set of points whose distances from two foci have constant sum;
. - Hyperbola
- Set of points whose distances from two foci have constant difference;
. - Eccentricity
: circle, ellipse, parabola, hyperbola.
Extra questions & answers
Write the equation of a circle with centre
Find the centre and radius of
Completing squares:
Define a parabola.
A parabola is the set of all points in a plane equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.
For
Comparing with
Define an ellipse and state the relation among
An ellipse is the set of points the sum of whose distances from two foci is constant; for
Give the eccentricity and latus rectum of an ellipse.
Eccentricity
For
Define a hyperbola and state the relation among
A hyperbola is the set of points the difference of whose distances from two foci is constant; for
For
What is the latus rectum of an ellipse and a hyperbola?
For both, the length of the latus rectum is