Equations of circles 1 November 5, 2018 Aug 215:12 PM L.O. To be able to find the equation of a circle 05/11/18 Starter Complete the square for the following: a) x 2 + 10x 4 b) x 2 5x +2 c) x 2 +6x d) x 2 19x Aug 215:12 PM L.O. To be able to find the equation of a circle 05/11/18 Example A circle has centre (0, 0) and a radius of 13. Does the following points lie inside the circle, outside of the circle or on the circumference of the circle? a) (12, 5) b) (9, 9)
Transcript
Equations of circles
1
November 5, 2018
Aug 215:12 PM
L.O. To be able to find the equation of a circle 05/11/18Starter
Complete the square for the following:
a) x2 + 10x 4
b) x2 5x + 2
c) x2 + 6x
d) x2 19x
Aug 215:12 PM
L.O. To be able to find the equation of a circle 05/11/18Example
A circle has centre (0, 0) and a radius of 13. Does the following points lie inside the circle, outside of the circle or on the circumference of the circle?
a) (12, 5)
b) (9, 9)
Equations of circles
2
November 5, 2018
Aug 215:12 PM
L.O. To be able to find the equation of a circle 05/11/18
You should know from GCSE that the equation of a circle with centre (0, 0) and radius r, is:
x 2 + y 2 = r 2
Example
A circle with centre (0, 0) and radius 5, is translated by the vector .
Find the equation of the circle after the translation.
Aug 215:12 PM
L.O. To be able to find the equation of a circle 05/11/18
The equation of a circle with centre (a, b) and radius r, is:
(x a) 2 + (y b) 2 = r 2
Quick questions
Write down the equation of the circles with:
a) Centre (5, 6) and radius 4
b) Centre (2, 3) and radius √7
c) Centre (5, 11) and radius 2π
Equations of circles
3
November 5, 2018
Aug 215:12 PM
L.O. To be able to find the equation of a circle 05/11/18Example
Write the equation of the circle x2 2x + y2 + 4y + 1 = 0 in the form (x a)2 + (y b)2 = r2
Aug 215:12 PM
L.O. To be able to find the equation of a circle 05/11/18Example
Find the equation of the circle that has a line segment from (7, 1) to (1, 3) as the diameter.
