Coordinate Geometry

Question 1

What is the equation of a circle?

Answer 1

(x-a)^2 + (y-b)^2 = r^2

Question 2

What would this circles centre and radius be;

(x-5)^2+(x+9)^2=81

Answer 2

centre= (5,-9)
radius= 9

Question 3

What is the first circle theorem rule?

Answer 3

The angle at the circumference in a semi-circle is always a right-angle.

Question 4

What is the second circle theorem rule?

Answer 4

The opposite angles in a quadrilateral always add up to 180 degrees.

Question 5

What is the third circle theorem rule?

Answer 5

The angle subtended by an arc is double the angle subtended at the circumference.

Question 6

What is the fourth circle theorem rule?

Answer 6

The angle at the circumference subtended by the same arc are equal.

Question 7

What is the fifth circle theorem rule?

Answer 7

The angle between a tangent and the radius is always 90 degrees.

Question 8

What is the sixth circle theorem?

Answer 8

The distance from the meeting point of two tangents to the points where the tangents meet the circle are the same for both tangents.

Question 9

How would you write a circles equation if it has a centre of (-2,0) and a radius of 11.

Answer 9

equation= (x+2)^2+y^2=121

Question 10

How would you write a circles equation if it had a centre of (8,-4) and a radius of V5 ( ‘V’ is a square root).

Answer 10

equation= (x-8)^2+(x+4)=5

Question 11

Name the first way you can tell an equation is not be a circle.

Answer 11

If the equation has a negative coefficient infront of ‘x’ or ‘y’, such as -6x or -y.

Question 12

Name the second way you can tell an equation is not a circle.

Answer 12

If ‘x’ and ‘y’ have different coefficients infront of them, such and 3x and y, or x and 2y.

Question 13

Name the third way you can tell an equation is not a circle.

Answer 13

Anything with an ‘x’ and ‘y’ multiplied together (xy), such as 3xy.