Circles Flashcards
When asked for which values of ( ) represent a circle
Make the equation of the radius greater than zero
What is the equation of a circle with centre (0,0)
X2 + y2 = r2
If you are given two points and you need to find the equation of the circle
Use distance formula or Pythagoras to determine radius and use centre to create equation
What are the three options for problems involving circles
D=r - the point lies on the circle
D>r - the point lies outside the circle
D<r - the point lies inside of the circle
How to find the equation of a tangent to a circle
- write down the centre of the circle
- calculate the gradient using new point and tangent point
- calculate perpendicular gradient
- use the tangent point and perpendicular gradient in straight line formula to find tangent equation
What does a repeated root mean
Tangent
If there are 2 roots
B2-4ac>0
If there is one/repeated root
b2-4ac=0
If there are no roots
b2-4ac<0
How to determine intersection of circles
-write down the centres of both circles - calculate the distance between them (D)
- calculate the radius of both circles (r1 and r2)
The circles do not touch
D> r1+r2
The circles touch externally
D=r1+r2
The circles meet at two distinct points
r1+r2> D
The circles touch internally
D=r1-r2
Or the distance is equal to the larger distance minus the smaller distance
The circles do not touch
D< r1+r2
Circles through three given points - possibility one
- the triangle is right angled (if perpendicular grad =-1) the hypotenuse of the triangle is the diameter of the circle
- find midpoint of hypotenuse this is the centre
- find distance from any of the points to the centre this is the radius
Circles through three given points - possibility two
- triangle is not right angled
- find equation of 2 perpendicular bisector
- find the point of intersection - centre
- find the distance from the centre to any of the points - radius
