1. THE HIGHER MATHEMATICS CLASS
WELCOME TO
THE HIGHER MATHEMATICS CLASS

2. OBSERVE THE PICTURE CAREFULLY
TELL ME THE SHAPE OF WHEEL.

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

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

5. 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

6. Y A B X O

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

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

9. 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= at (x1,y1) becomes xx1+yy1 +g(x+x1)+f(y+y1)+c=0

10. 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 .

11. Evaluation
1.What is the tangent of the Circle?

12. 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.

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