Coordinate & circle geometry Flashcards
what is the construction form
how do you find the distance between 2 points (two ways)
How do you find the midpoint
equation of a circle
how would you find the equation of a circle when not given a letter in an equation
how would you solve this question
formula to find the gradient (m)
parallel and perpendicular lines
how to find the point of intersection of two lines
when are two quantities in direct proportion
how to solve this perpendicular bisector question
steps:
1) find the q by finding the gradient of XY
2) find the midpoint of XY
3) substitute the x and y values from the midpoint into the perpendicular equation to find b
perpendicular bisectors always…
go through the midpoint
how to find the radius of this question
steps:
1) pythagoras theorem using the x value of the point on the circle + the x value of the equation of the circle
2) same for the y value
3) get r
how to show that this line doesnt go through the circle
steps:
1) start as if you were to prove that is does and sub in what y = into the circle equation
2) expand and simplify
3) put it into the discriminant to test for roots
4) if it is less than 0 then it has no roots
what is the discriminant equation and when do i use it
use it when proving whether lines meet or there are roots
properties of a tangent
properties of a chord
steps:
1) find the gradient of AB
2) find the gradient of BC
3) multiply them together if the 2 gradients together = -1 then they are perpendicular
this uses the circle theory that a triangle within a semi-circle where it touches the circle will be a 90 degree angle
TOOLS
T for TOOLS
triangle area
can only use it if an angle is between two variables
first O for TOOLS
Sector area
how to convert degrees to radians
second O for TOOLS
Arc length
L for TOOLS
The last resort -> cosine rule
S for TOOLS
Sine Rule
