Coordinate Geometry

Question 1

Equation of a circle

Answer 1

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

Question 2

Determining whether two circles intersect

Answer 2

Find the distance, d, between centres of circles
Find the radii, r1 and r2, of the circles
If r2-r1 < d < r1 + r2, two intersections
If d = r1 + r2, one intersection
if d > r1 + r2, no intersections

Question 3

Finding points of interesection

Answer 3

Rearrange both circle equations so one side = 0
Solve simultaneously, x^2 and y^2 terms cancel into
y = mx + c, the intersections lying on this line
Substitute linear equations into either circle equation
Solve for coordinates x, then y.