If you want to compare gradients of two lines, what must you do?
Put Y on its own in both.
What is the gradient if a line goes straight up?
It isn’t infinite, but undefined.
What are the circle theorems that you may need to know ?
Angles in a semicircle= 90
Chord bisector will go through the centre.
A tangent to the circle is perpendicular to a point.
What would the equation of a circle with centre (5,-3) and radius 6 be?
(X-5)² +Y+3)² = 36
What are the coordinates of the centre of (x+4)² +y² ?
What would you do if you had to find the equation of a circle with a given centre that went through a given point?
Find the distance between the centre and the point and make that your radius.
What do you do if you know a circle just touches one of the axis and goes through the other at two points and you have to find the equations of it?
Find the midpoint of the two points where the circle goes through one of the axis. This will provide one of the values of the coordinate of the centre and give the radius.
Use the general equation of the circle and substitute in the values you know. You should be able to find the second part of centre coordinate.
Understand that the circle could be above or below one the axis and provide two equations to show this.
How would you show that a line is a tangent, intersecter or misses a circle or curve?
Substitute the line equation into that of the curve. A quadratic equation should be produced. If there are two different values, it touches at two points. One value repeated means it is a tangent.
If it can’t be solved, they don’t touch.
How would the equation of the tangent to a circle be found?
Find the gradient of the centre to the tangent and this will be perpendicular to the gradient you want.