THE HIGHER MATHEMATICS CLASS WELCOME TO THE HIGHER MATHEMATICS CLASS

OBSERVE THE PICTURE CAREFULLY TELL ME THE SHAPE OF WHEEL.

THE CIRCLE CHAPTER -4 EXERCISE -4.2 BOOK BY AKKHOR POTRA

LEARNING OUTCOME YOU CAN KNOW FROM THIS CHAPTER 1. About the tangent of the Circle 2. Equation of a tangent and normal of a circle at a fixed point on the circle. 3. Equation of a tangent and normal of a circle at a fixed point outside the circle.

EVERY STRAIGHT LINE CUTS THE CIRCLE AT TWO POINTS EVERY STRAIGHT LINE CUTS THE CIRCLE AT TWO POINTS . OBSERVE THE FOLLOWING FIGURES. Y A B X O

Y A B X O

X Y THIS POINT IS CALLED COINCIDENT POINT THIS IS CALLED TANGENT A,B O

ANOTHER CONDITION FOR TANGENCY: THE PERPENDICULAR DISTANCE FROM THE CENTER ON THE TANGENT IS EQUAL TO THE RADIUS. RADIUS

Necessary formula for circle. 1.The Equation of tangent of the circle at (x1,y1) becomes xx1+yy1=r2 2.The Equation of tangent of the circle x2+y2+2gx+2fy+c=0 at (x1,y1) becomes xx1+yy1 +g(x+x1)+f(y+y1)+c=0

Group Work 1.Find the equation of the tangent of the circle x2+y2=8 at(2,-2). 2. Find the equation of the tangent of the circle x2+y2 -2x-4y+4 =0 at(1,-2).. 3.Determine the value of b if the line3x+by-1=0 touches the circle x2+y2 -8x-2y+4 =0 .

Evaluation 1.What is the tangent of the Circle?

HOME WORK 1.Find the equation of the tangent of the circle x2+y2=8 at(-2,-2). 2. Find the equation of the tangent of the circle x2+y2 -3x+10y-15 =0 at(4,-11).. 3.Determine the value of k if the line3x+4y-k=0 touches the circle x2+y2 =10x.

EUCLID ,FATHER OF GEOMETRY THANKS TO ALL EUCLID ,FATHER OF GEOMETRY