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INTRODUCTION

• A conic section or a conic is locus of a point ,which moves such that its distance from a fixed point is in constant ratio to its distance from a fixed straight line not passing through the fixed point.The fixed point is called focus and the fixed line is called directrix.The constant ratio is called ecentricity which is denoted by 'e' .
• when e=1,the conic is parabola.When e<1,the conic is an ellipse.When e>1,the conic is hyperbola.
• The line of symmetry of conic is called its AXIS
• The point of intersection of conic with its AXIS is called VERTEX.
• The chord passing through focus and perpendicular to AXIS is called LATUS RECTUM.

GENERAL EQUATION OF CONIC

STANDARD EQUATION OF PARABOLA

• Let P be a moving point and Abe the origin.Here SZ is the axis of the parabola.Now, the middle point of SZ say A will lie on the locus of P i.e ,AS=AZ.

Let    AS=AZ.

Let     AS=a,then ZA=a
let(x,y) be the coordinates of point P

LATUS RECTUM OF A PARABOLA

• Any chord of parabola y^{2=4ax which is perpendicular to its axis is called double ordinate.}

DIFFERENT FORMS OF PARABOLA

FOCAL CHORD

• Any chord  to parabola y^{2=4ax which passes through the focus is called the focal chord of the parabola .}

 

FOCAL DISTANCE OF ANY POINT

The distance between point P on the conic and the focus S is called the focal distance i.e PS

 Therefore focal distance of the parabola =PS=a+x