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# I've got some C2 coordinate geometry Qs! watch

1. 16) The points A(-5,5), B(1,5), C(3,3), D(3,-3) lie on a circle. Find the equation of the circle.

12) The points R(-4,3), S(7,4) and T(8,-7) lie on a circle.
a) Show that triangle RST has a right angle. (Ok, I can do this bit)
b) Find the equation of the cirlce. (Now what?)

11) The points A(-4,0), B(4,8) and C(6,0) lie on a circle. The lines AB and BC are chords of the circle. Find the coordinates of the centre of the circle. (So do I find the eqn of AB and then BC and solve simultaneously, or what?)

10) Show that (0,0) lie inside the circle (x-5)² + (y+2)² = 30. (What does that mean? -Inside- the cirlce??)
2. 10) Find the extreme points of the circle.
It has centre (5,-2), and radius rt(30).
So, horizontally, it stretches from 5-rt(30) to 5+rt(30), and in decimal form that's, -0.5 to 10.5
Vertically, it goes from -7.5 to 3.5 (using -2-rt(30) and -2+rt(30) )

In both cases, the origin (0,0), is within the circumference of circle, and hence lies inside the circle.
3. (Original post by *girlie*)
16) The points A(-5,5), B(1,5), C(3,3), D(3,-3) lie on a circle. Find the equation of the circle.

12) The points R(-4,3), S(7,4) and T(8,-7) lie on a circle.
a) Show that triangle RST has a right angle. (Ok, I can do this bit)
b) Find the equation of the cirlce. (Now what?)

11) The points A(-4,0), B(4,8) and C(6,0) lie on a circle. The lines AB and BC are chords of the circle. Find the coordinates of the centre of the circle. (So do I find the eqn of AB and then BC and solve simultaneously, or what?)

10) Show that (0,0) lie inside the circle (x-5)² + (y+2)² = 30. (What does that mean? -Inside- the cirlce??)
For 11) I think you have to find the equation of the normal to the chords and then solve them simultaneously to get the centre. From the centre you can deduce the radius.
4. 16) Find the midpoint of AB and the gradient to the normal to the line AB. From this, using y-y1=m(x-x1), you can find an equation of the line that passes through the centre.

Repeat the same procedure, except use the line BC. This will get you another equation for a line passing through the centre. Solve these two equations to work out the centre co-ordinates, then to find the radius use the difference between the centre and one of the points and pythagoras' rule- for example if you had a point on the circle that was (3,5) and you found the centre of the circle to have coordinates (1,2) then:

r²=(x-x1)²+(y-y1)²
r²=(3-1)²+(5-2)²
r²=4+9
r = √13

You can use this message to solve the other questions as well...

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