Analytic Geometry: Standard and General Form of a Cirle

Definition of A circle

1. ANALYTIC GEOMETRY ENGR. RENE M. INSON

2. CIRCLE Is the locus of a point which moves at a constant distance from a fixed point called its center.   Radius – The constant distance of any point from the center .   If the center is at the origin: Then,   General Equation: If  

3. Example: 1 . Reduce to standard form and draw the circle whose equation is . 2 . a. Find the equation of a circle with center at and tangent to the line . b. Find the equation of the line parallel to the 1’st line and tangent to the circle. 3. Find the equation of a circle with the points and as the ends of a diameter. Find the area of a circle.   4 . Find the equation of the lines tangent to the circle through the point  

4. 1 . Reduce to standard form and draw the circle whose equation is .  

5. 2 . a. Find the equation of a circle with center at and tangent to the line . b. Find the equation of the line parallel to the 1’st line and tangent to the circle.  

6. 3 . Find the equation of a circle with the points and as the ends of a diameter. Find the area of a circle .  

7.  4. Find the equation of the line tangent to the circle through the point  

8. Three conditions determine a circle : From : 3 constants: Examples : 1. Find the equations of the circle passing through , and . 3 . Find the equation of the circle passing through and and with center on . 4 . Show that the circles and are tangent externally then find the area and circumference of each circle. Draw the circles. 5 . Find the equation of the circle inscribed in a triangle. If the triangle has its sides on the lines:  

9. 1. Find the equations of the circle passing through , and .  

10. 3 . Find the equation of the circle passing through and and with center on .  

11. 4 . Show that the circles and are tangent externally then find the area and circumference of each circle. Draw the circles .  

12. 5 . Find the equation of the circle inscribed in a triangle. If the triangle has its sides on the lines: