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I've got some C2 coordinate geometry Qs! watch

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    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??)
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    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.
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    (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.
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    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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