circles

Question 1

what is the equation of a circle with centre (a,b) and radius r?

Answer 1

(x - a)^2 + (y - b)^2 = r^2

Question 2

what features do you need to add on a sketch of a circle?

Answer 2

min/max x and y values on the circumference, found by adding or subtracting r from one of the values in the centre coordinate and the centre itself

Question 3

how do you make an =0 equation look like a normal circle equation?

Answer 3

complete the square for x and y separately and then add the r values together and rearrange into the standard format

Question 4

how do you find the intersection of straight lines and circles?

Answer 4

sub in the straight line equation into the circle by. making x or y the subject, then just solve the resultant quadratic.
to test how many intersections there will be, sub the line eq. into the circle eq. and use the discriminant following the same rules as normal (>0: 2 ints, =0: 1 int, <0: no ints)

Question 5

how do you find equations of normals/tangents?

Answer 5

use the centre and the point of intersection of the normal to fing the normal eq. (grdt. is change in y over change in x, sub into
y - y1 = m(x - x1).
to find tangent, use inverse reciprocal of normal gradient and the use the int. point to fid an equation as above

Question 6

how do you verify a point lies on a circle?

Answer 6

just sub the x and y values into the circle equation

Question 7

what is the best practice when solving circle geometry problems?

Answer 7

draw a diagram and visualise. triangulation and circle theorems will help without end once you can see them.