Circle Flashcards
What is a circle?
A circle is aloud of points equidistant from a fixed point (the centre).
What does “C” represent?
- Is a set of points at distance r
From the origin - P (x,y) is marked on the circumference
What does “R” represents?
Radius
- is x^2 + y^2 = r^2
The equation of a circle with centre (0,0) is?
is x^2 + y^2 = r^2
Distance formula
D = -/ (x2 - x1)^2 + ( y2- y1)^2
Simpler version of distance formula in circle
D^2 = (x2 - x1)^2 + (y2 - y1)^ 2 to find r^2 directly
The equation of a circle with a centre (a,b) and radius r is ….
The equation of a circle with a centre (a,b) and radius r is (x - a)^2 + (y - b)^2 = r^2
Concentric circles
Concentric circles have the same centre
Find diameter steps
- Midpoint to find the centre
- Distance formula to find the radius
- Equation of the circle
What is the general equation of a circle with centre (-g,-f) and radius -/ g^2 + f^2 - c, provided that g^2 + f^2 - c > 0
The equation x^2 + y^2 + 2gx + 2fy + c = 0 is the General equation of a circle with centre (-g,-f) and radius -/ g^2 + f^2 - c, provided that g^2 + f^2 - c > 0
Equation to find a tangent to a circle steps…
- Gradient of the radius
- Gradient of tangent is perpendicular to radius
- Sub in equation of the tangent
Proving points that lies on the circumference of the circle
- Sub in x and y
- it should equal the original equation radius
After proving the point lies on the circumference of the circle
- Gradient of radius of the two points
- Tangent gradient (perpendicular to radius)
- Sub into equation of the tangent
Why do we use the discriminant?
The value of the discriminant to find how many points of intersection there are
The value of the discriminant to find two points of intersection
b^2 - 4ac > 0
