# Circle Flashcards

1
Q

What is a circle?

A

A circle is aloud of points equidistant from a fixed point (the centre).

2
Q

What does “C” represent?

A
• Is a set of points at distance r
From the origin
• P (x,y) is marked on the circumference
3
Q

What does “R” represents?

A

• is x^2 + y^2 = r^2
4
Q

The equation of a circle with centre (0,0) is?

A

is x^2 + y^2 = r^2

5
Q

Distance formula

A

D = -/ (x2 - x1)^2 + ( y2- y1)^2

6
Q

Simpler version of distance formula in circle

A

D^2 = (x2 - x1)^2 + (y2 - y1)^ 2 to find r^2 directly

7
Q

The equation of a circle with a centre (a,b) and radius r is ….

A

The equation of a circle with a centre (a,b) and radius r is (x - a)^2 + (y - b)^2 = r^2

8
Q

Concentric circles

A

Concentric circles have the same centre

9
Q

Find diameter steps

A
1. Midpoint to find the centre
2. Distance formula to find the radius
3. Equation of the circle
10
Q

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

A

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

11
Q

Equation to find a tangent to a circle steps…

A
3. Sub in equation of the tangent
12
Q

Proving points that lies on the circumference of the circle

A
1. Sub in x and y

- it should equal the original equation radius

13
Q

After proving the point lies on the circumference of the circle

A
3. Sub into equation of the tangent
14
Q

Why do we use the discriminant?

A

The value of the discriminant to find how many points of intersection there are

15
Q

The value of the discriminant to find two points of intersection

A

b^2 - 4ac > 0

16
Q

The value of the discriminant to find one points of intersection

A

b^2 - 4ac = 0

• (i. e the line is a tangent to the circle)
17
Q

The value of the discriminant to find no points of intersection

A

b^2 - 4ac < 0