Ch.6 Circles

Question 1

what is the equations of a circle with the centre (0,0)?

Answer 1

x² + y² = r²

Question 2

what is the equations of a circle with the centre (a,b)?

Answer 2

( x - a )² + ( y - b )² = r²

Question 3

how many times can a straight line intersect a circle?

Answer 3

Once, twice or zero times

Question 4

at intersection, what is a tangent to a circle perpendicular to?

Answer 4

its radius

Question 5

what will the perpendicular bisector of a chord go through?

Answer 5

the centre of the circle

Question 6

what is a circumcircle?

Answer 6

a circle that has been drawn to meet all 3 vertices of a triangle

Question 7

what is the centre of a circumcircle called?

Answer 7

a circum centre

Question 8

in a circumcircle what is a right angled triangles hypotenuse?

Answer 8

the circumcircle’s diameter

Question 9

what are 2 ways to state that a right angled triangles hypotenuse in a circumcircle is the circles diameter?

Answer 9

1 - if angle ABC = 90° then AC is the diameter
2 - angle in semicircle is always 90°

Question 10

how would you find the centre of any circle given any 3 points on circumference?

Answer 10

First find the equations of perpendicular bisectors of 2 chords then find the coordinates of their intersection

Question 11

what is the third form that the equations of a circle can be given?

Answer 11

the expanded version of a circle with centre (-f,-g) :
x² + y² + 2fx + 2gy + c = 0