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# Conics Sections

maths in day to day life

by

Tweet## nitha sreedharan

on 10 January 2013#### Transcript of Conics Sections

Conic Sections INTRODUCTION THE END Before knowing what a conic section is we shall learn what a double-napped cone is.

Let a fixed line l, and another line m intersecting it at any point V,& inclined to l at an angle

Suppose m rotates around l, such that the folllow-

ing figure is formed: What is a conic section? CIRCLE Varieties of Conic Sections Eccentricity Thank You for watching...

..Hopes you enjoyed it. This is a presentation based on the

chapter CONIC SECTIONS. This passes through various topics in the chap-

ter, as well as other related stuffs like,parabolas & ellipses& circles in

day to day life.

Please Enjoy! CIRCLE Submitted by,

NITHA SREEDHARAN Circle: is the set of all points in a plane that are equidistant fixed point in the plane. radius O(centre) Let centre,O be (h,k) & centre be

joined to point P(x,y), such that

OP is the radius of the circle.

Then, equation of the circle is P (x-h)^2 + (y-k)^2 = r^2 Parabola where, V=Vertex

l=axis

m=generator let a plane cut the nappe of the cone at an angle . when = 90 degree , section = circle

When < < 90 degree, section = ellipse

When = ,section = parabola

When 0 < or= < ,section = hyperbola A parabola is the set of all points in a plane that are equidistant from a fixed point in the plane. The fixed line is called the directrix & the fixed point is called the Focus (F). The line passing through F & perpen-dicular to the directrix is known as the axis.The line that joins two points on the parabola passing through the focus is called the Latus rectum. Equation of the

parabola;

y^2 = 4ax Equation of the

parabola;

y^2 = -4ax Equation of the

parabola;

x^2 = 4ay Equation of the

parabola;

x^2 = -4ay Standard equations of Parabola Ellipse; from a is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant. The fixed points are called Foci(F1 & F2).The line segment that goes through both the foci is known as the Major Axis(AB). Its midpoint is called the centre(O).The line passing through the centre is called the Minor axis(CD). Standard Equations of

ELLIPSE (-c,0) (0,0) (c,0) (a,0) (-a,0) x^2 + y^2 a^2 b^2 = 1 Eccentricity of an ellipse: The eccentricity of an ellipse is the ratio of the distances from the centre of the ellipse to one of the foci and to one of the vertices of the ellipse e = c/a Eccentricity of hyperbola; The eccentricity of a hyperbola is the distance between the centre

of the hyperbola to one of its foci

& to one of the vertices of the hyperbola. CONIC SECTIONS IN

DAY 2 DAY LIFE Ellipses (0,0) (0,a) (0,-a) (0,-c) (0,c) From Sun to bubbles..... Circles x^2 + y^2 b^2 a^2 = 1 Parabola Gallery Hyperbola It is the set of all the points in a plane, the difference of whose distances from two fixed points in the plane is a constant. The two fixed points are the foci(F1 & F2) of the hyperbola. The midpoint of the line segment joining the foci is called

the Centre(0). The axis

passing through the foci

are called Transverse axis

(XX').The line segment

(axis) through the centre,

perpendicular to the

transverse axis is the

Conjugate axis.

x^2 - y^2 a^2 b^2 = 1 (a,0) (c,0) (-c,0) (0,0) (-a,0) (0,-c) (0,c) (0,a) (0,-a) (0,0)

Full transcriptLet a fixed line l, and another line m intersecting it at any point V,& inclined to l at an angle

Suppose m rotates around l, such that the folllow-

ing figure is formed: What is a conic section? CIRCLE Varieties of Conic Sections Eccentricity Thank You for watching...

..Hopes you enjoyed it. This is a presentation based on the

chapter CONIC SECTIONS. This passes through various topics in the chap-

ter, as well as other related stuffs like,parabolas & ellipses& circles in

day to day life.

Please Enjoy! CIRCLE Submitted by,

NITHA SREEDHARAN Circle: is the set of all points in a plane that are equidistant fixed point in the plane. radius O(centre) Let centre,O be (h,k) & centre be

joined to point P(x,y), such that

OP is the radius of the circle.

Then, equation of the circle is P (x-h)^2 + (y-k)^2 = r^2 Parabola where, V=Vertex

l=axis

m=generator let a plane cut the nappe of the cone at an angle . when = 90 degree , section = circle

When < < 90 degree, section = ellipse

When = ,section = parabola

When 0 < or= < ,section = hyperbola A parabola is the set of all points in a plane that are equidistant from a fixed point in the plane. The fixed line is called the directrix & the fixed point is called the Focus (F). The line passing through F & perpen-dicular to the directrix is known as the axis.The line that joins two points on the parabola passing through the focus is called the Latus rectum. Equation of the

parabola;

y^2 = 4ax Equation of the

parabola;

y^2 = -4ax Equation of the

parabola;

x^2 = 4ay Equation of the

parabola;

x^2 = -4ay Standard equations of Parabola Ellipse; from a is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant. The fixed points are called Foci(F1 & F2).The line segment that goes through both the foci is known as the Major Axis(AB). Its midpoint is called the centre(O).The line passing through the centre is called the Minor axis(CD). Standard Equations of

ELLIPSE (-c,0) (0,0) (c,0) (a,0) (-a,0) x^2 + y^2 a^2 b^2 = 1 Eccentricity of an ellipse: The eccentricity of an ellipse is the ratio of the distances from the centre of the ellipse to one of the foci and to one of the vertices of the ellipse e = c/a Eccentricity of hyperbola; The eccentricity of a hyperbola is the distance between the centre

of the hyperbola to one of its foci

& to one of the vertices of the hyperbola. CONIC SECTIONS IN

DAY 2 DAY LIFE Ellipses (0,0) (0,a) (0,-a) (0,-c) (0,c) From Sun to bubbles..... Circles x^2 + y^2 b^2 a^2 = 1 Parabola Gallery Hyperbola It is the set of all the points in a plane, the difference of whose distances from two fixed points in the plane is a constant. The two fixed points are the foci(F1 & F2) of the hyperbola. The midpoint of the line segment joining the foci is called

the Centre(0). The axis

passing through the foci

are called Transverse axis

(XX').The line segment

(axis) through the centre,

perpendicular to the

transverse axis is the

Conjugate axis.

x^2 - y^2 a^2 b^2 = 1 (a,0) (c,0) (-c,0) (0,0) (-a,0) (0,-c) (0,c) (0,a) (0,-a) (0,0)