Grade 10 Academic MPM 2 D Unit 2

Grade 10 Academic (MPM 2 D) Unit 2: Analytic Geometry Equation of a Circle Mr. Choi © 2017 E. Choi – MPM 2 D - All Rights Reserved

Circle A circle is the set of all points in a plane that are the same distance from a fixed point, the centre O. The distance from any point on the circle to the centre is called the radius r. r O Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Circle If the centre of the circle is at the origin of the x-y plane and the radius is r units, then , which is equivalent to . r O Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Circle This equation, , is the equation of a circle with centre (0, 0) and radius r. This equation, is the equation of a circle with centre and radius r. Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 1 a: Write the equation of a circle with the given centre and radius, illustrate with a diagram. a) with centre (0, 0) and a radius of 6. Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 1 b: Write the equation of a circle with the given centre and radius, illustrate with a diagram. b) with centre (1, -2) and a radius of 4. Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Recall: Distance between two points on a Plane Given two points The distance d, is: Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 2: Write the equation of a circle with centre the origin and passes through A(3, -4). What are the coordinates of the other end point of the diameter that passes through (3, -4)? Illustrate with a diagram. O A Another end point of the diameter containing (3, -4) is at (-3, 4). Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 3: Write the equation of a circle with centre C(-3, 2) and passes through D(1, 4). Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 4: A stone is dropped into a pond and sends out a circular ripple whose radius increases by 6 cm/s. Find the equation of the circle 10 seconds after the stone is dropped. If the radius grows by 6 cm/s, then after 10 sec the radius is 60 cm The equation of the circle at this time is Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 5: Given the equation of a circle with center C (5, -7)and passes through the point P (2, -3), determine the highest, lowest, leftmost and rightmost points. P C Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

Homework Work sheet: Equation of a Circle Text: • P. 156 #8 -12 • Check the website for updates Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved

End of lesson Equation of a Circle © 2017 E. Choi – MPM 2 D - All Rights Reserved