Circle

Question 1

What is a circle?

Answer 1

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

Question 2

What does “C” represent?

Answer 2

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

Question 3

What does “R” represents?

Answer 3

Radius

• is x^2 + y^2 = r^2

Question 4

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

Answer 4

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

Question 5

Distance formula

Answer 5

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

Question 6

Simpler version of distance formula in circle

Answer 6

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

Question 7

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

Answer 7

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

Question 8

Concentric circles

Answer 8

Concentric circles have the same centre

Question 9

Find diameter steps

Answer 9

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

Question 10

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

Answer 10

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

Question 11

Equation to find a tangent to a circle steps…

Answer 11

1. Gradient of the radius
2. Gradient of tangent is perpendicular to radius
3. Sub in equation of the tangent

Question 12

Proving points that lies on the circumference of the circle

Answer 12

1. Sub in x and y

- it should equal the original equation radius

Question 13

After proving the point lies on the circumference of the circle

Answer 13

1. Gradient of radius of the two points
2. Tangent gradient (perpendicular to radius)
3. Sub into equation of the tangent

Question 14

Why do we use the discriminant?

Answer 14

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

Question 15

The value of the discriminant to find two points of intersection

Answer 15

b^2 - 4ac > 0

Question 16

The value of the discriminant to find one points of intersection

Answer 16

b^2 - 4ac = 0

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

Question 17

The value of the discriminant to find no points of intersection

Answer 17

b^2 - 4ac < 0