7 coordinate geometry of a circle

Question 1

How do you work out the centre of a circle from its diameter?

Answer 1

-Work out the midpoint of the diameter.

Question 2

What is a line segment?

Answer 2

-A finite point of a line with two distinct endpoints

Question 3

What is a perpendicular bisector of a line segment?

Answer 3

-Cuts the midpoint of a line segment at a right angle.

Question 4

What is the form of the equation of a circle and what can you find out from this?

Answer 4

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

centre is alb and radius is r

Question 5

How can you work out the equation of a circle with terms?

Answer 5

-complete the square.

Question 6

How does the discriminant link to circles?

Answer 6

• if it intersects at 1 point/ touches discriminant b^2-4ac=0
• If it intersects at two points discriminant b^2-4ac >0
• If it intersects at no points <0

Question 7

What is the property between a radius and a tangent?

Answer 7

-meet at right angle.

Question 8

What is the property between the perpendicular bisector and a chord of a circle?

Answer 8

-The perpendicular bisector of a chord will go through the centre of a circle.

Question 9

What is the property of a right angled triangle inside a circle?

Answer 9

-The hypotenuse is always the diameter

Question 10

How do you find the centre of the circle given any three points on the circumference?

Answer 10

-Find the where the perpendicular bisector of two chords intersect.

Question 11

How do you find the equation of two unknown tangents if the equation of the circle is given?

Answer 11

-Sub a form of equation into the circle and use discriminant to solve.