Straight line graphs and circles B1 ch5+6 Flashcards
Equation for finding the equation of a line when given gradient and one coordinate.
Y-Y1=M(X-X1)
When are two quantities in direct proportion?
When they increase at the same rate (straight line) and passes through the origin
How can the point of intersection of two straight lines be found?
Using simultaneous equations
Equation of circle which has a centre (0,0)
x^2+y^2=r^2
Equation of circle with centre (a,b)
(x-a)^2+(y-b)^2=r^2
How would you find the centre and radius of a circle when it is given in the extended form
Complete the square to put in (x-a)^2+(y-b)^2=r^2 format
How will you know when a line is a tangent to a circle
It will have a repeated solution so will only touch at one coordinate
How can you find the gradient of a tangent to a circle
A tangent is perpendicular to the radius which meets at the point of intersection
What is a chord
A line segment that joins two points on the circumference of a circle
What is special about the perpendicular bisector of a chord?
It goes through the centre of the circle
What is the circumcentre?
The centre of a circle which joins up the corners of a triangle
What is a circumcircle?
The circle which joins up the corners of a triangle
For a right angled triangle in a circle what is special about the hypotenuse?
It is also the diameter of the circle
How do you find the centre of a circle given any three points on the circumference?
- join the points to create a triangle
- find the perpendicular bisectors of each side of the triangle
- where they intersect is the middle of the circle
