The document discusses the perpendicular distance formula. It states that the shortest distance from a point to a line is the perpendicular distance. It provides the formula for finding the perpendicular distance as d=|Ax+By+C|/√(A^2 +B^2) where Ax+By+C=0 is the equation of the line. It gives an example of finding the equation of a circle given the equation of a tangent line and the center point.

1. Perpendicular Distance Formula

2. Perpendicular Distance Formula The shortest distance from a point to a line is the perpendicular distance.

3. Perpendicular Distance Formula The shortest distance from a point to a line is the perpendicular distance.

4. Perpendicular Distance Formula The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0

5. Perpendicular Distance Formula The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d

6. Perpendicular Distance Formula The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d

7. Perpendicular Distance Formula e.g. Find the equation of the circle with tangent 3 x – 4 y – 12 = 0 and centre (1,4). The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d

8. Perpendicular Distance Formula e.g. Find the equation of the circle with tangent 3 x – 4 y – 12 = 0 and centre (1,4). The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d

9. Perpendicular Distance Formula e.g. Find the equation of the circle with tangent 3 x – 4 y – 12 = 0 and centre (1,4). The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d 3 x – 4 y – 12 = 0

10. Perpendicular Distance Formula e.g. Find the equation of the circle with tangent 3 x – 4 y – 12 = 0 and centre (1,4). The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d 3 x – 4 y – 12 = 0 r

11. Perpendicular Distance Formula e.g. Find the equation of the circle with tangent 3 x – 4 y – 12 = 0 and centre (1,4). The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d 3 x – 4 y – 12 = 0 r

12. Perpendicular Distance Formula e.g. Find the equation of the circle with tangent 3 x – 4 y – 12 = 0 and centre (1,4). The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d 3 x – 4 y – 12 = 0 r

13. Perpendicular Distance Formula e.g. Find the equation of the circle with tangent 3 x – 4 y – 12 = 0 and centre (1,4). The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d 3 x – 4 y – 12 = 0 r

14. Perpendicular Distance Formula e.g. Find the equation of the circle with tangent 3 x – 4 y – 12 = 0 and centre (1,4). The shortest distance from a point to a line is the perpendicular distance. Ax + By + C = 0 d 3 x – 4 y – 12 = 0 r

15. If has different signs for different points, they are on different sides of the line.

16. If has different signs for different points, they are on different sides of the line. Ax + By + C = 0

17. If has different signs for different points, they are on different sides of the line. Ax + By + C = 0 Ax + By + C > 0

18. If has different signs for different points, they are on different sides of the line. Ax + By + C = 0 Ax + By + C > 0 Ax + By + C < 0

19. If has different signs for different points, they are on different sides of the line. Exercise 5E; 1b, 2cf, 5a, 6a, 7bd, 8b, 9abc, 10, 13, 14, 18* Ax + By + C = 0 Ax + By + C > 0 Ax + By + C < 0