short notes module 8 conic

SHORT NOTES MODULE 8: CONIC SECTIONS

Equation of Circles

Equations:

EQUATIONS

standard

general

( x − h)2 + ( y − k )2 = r 2

x2 + y2 + 2gx + 2fy + c = 0

centre,C = (h,k )

radius = r

centre,C = ( −g, −f )

Graph: y P(x, y) r Centre, C (h, k)

x

radius,r = g2 + f 2 − c

Parabola General Information: axis of symmetry 1. |p| is the length between vertex and focus.

2. |p| is the shortest distance between vertex and

parabola

Latus rectum

focus

directrix line.

3. Axis of symmetry is a line passes through vertex and focus.

4. Latus rectum is a line perpendicular to axis of symmetry and passes through focus.

5. Directrix is a line perpendicular to the axis of symmetry.

vertex directrix

Equations & Graphs:

p>0 ( y − k )2 = 4p ( x − h )

p<0 equations

p>0

( x − h )2 = 4p ( y − k )

p<0

Ellipse General Information:

Vertices 1)

Latus rectum

2) 3) 4)

center

Minor axis 5) 6)

Covertices

Foci

7)

Centre is a midpoint of vertices and midpoint of foci.

Vertices are endpoints on major axis.

Covertices are endpoints on minor axis.

Foci are points lie on major axis in between vertex and centre. It is not a midpoint of vertex and centre.

Major axis is a line passes through centre and foci.

Minor axis is a line passes through centre and perpendicular to major axis.

Latus rectum is a line perpendicular to major axis and passes through foci.

Major axis

Equations & Graphs:

equation ( x − h ) + ( y − k )2 = 1 2

a2

a>b

b2

;

a,b  0

a<b