[Audio] Hello everybody. Today I'm presenting my work to you through this PowerPoint.

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[Audio] As you have seen in this slide, the topic of my presentation is circle. I've made this presentation in the form of a video so pause when you want and have a look.

CIRCLE

[Audio] These are our major topic for today. So let's begin.

CIRCLE

IN THIS LESSON WE ARE GOING TO STUDY ABOUT EQUATION OF CIRCLE GENERAL EQUATION OF CIRCLE TANGENT AND NORMAL CONDITION OF TANGENCY AND SOME EXAMPLES WITH EXERCISES TO CONCLUDE

[Audio] As you know, circle is a geometric shape. In mathematics, a circle is a shape consisting of all points in a plane which are equidistance to the given fixed point which is it's centre. Have a look in the figure. This is the general introduction of what is a circle. I guess you guys have already learnt this in junior grades.

THE CIRCLE

SO WHAT IS A CIRCLE? IN SIMPLE LANGUAGE, A circle is a shape consisting of all points in a plane which are equidistance to the given fixed point i.e. Centre. And the distance between fixed point and the curved plane is radius. Diameter is the straight line passing through Centre and joining two any points in a circle.

Figure: showing a circle

[Audio] Equation of circle at h, k and radius 'a' is x minus h whole square plus y minus k whole square is equal to a square. Please have a look at note.

Formulae

Equation of a circle: If the Centre of the circle is at A( h,k ) and radius is ‘a’ then the equation of the circle is given by (?-h) 2 + (?- k) 2 = a 2 Note ; I f the Centre is at origin then h=k=0. Then the equation of circle be ? 2 + ? 2 = a 2

[Audio] Now the equation of circle in diameter form is x minus x1 common x minus x2 plus y minus y1 common y minus y2 is equal to zero. Pause the video to look at the slide how that came.

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o

?

F (?1, ?1)

A(?,?)

D(?2, ?2)

[Audio] Here is the general equation of circle, Its is x square plus y square plus 2 g x plus 2 f y plus c is equal to zero. From equation 2 we found out that the radius r is equal to square root g square plus f square minus c.

[Audio] Tangent is a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point.

What is a tangent? T angent is a straight line which just touches the curve at a given point. In this figure ATB is tangent at T. The point T is called the point of contact. NOTE: The tangent should only touch the only one point in a circle.

[Audio] Normal is a straight line which is perpendicular to the tangent.

Normal Normal is a straight line which is perpendicular to the tangent . In this figure, The straight line BOC is the normal to the Tangent AB.

A

B

O

C

[Audio] A line y is equal to m x plus c will be tangent to the circle is the length of the perpendicular from the centre 0,0 to the line y is equal to m x plus c is equal to the radius of the circle. That is c is equal to plus minus a square root 1 plus m square.