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    A bit confused about these:

    9) The line y=2x-2 meets the circle (x-2)²+(y-2)²=20 at A and B.
    a) Find the coordinates of A and B. ---> Done that (0,-2), (4,6).
    b) Show that AB is a diameter of the circle. (How would you prove this?)

    10) The line x+y=a meets the circle (x-p)²+(y-6)²=20 at (3,10), where a and p are constants.
    a) Work out the value of a.
    b) Work out the two possible values of p.
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    9. b) The radius of the circle is √20- agreed?
    So the diameter would be 2√20 = 4√5

    The length AB = √ [(4-0)²+(6+2)²] = √(16+64) = √80 = √16.√5 = 4√5

    The length AB is equal to the length of the diameter, hence AB is a diameter of the circle.
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    Ohh, thank you! Actually, I have one more...

    1) The line y=2x-8 meets the coordinate axes at A and B. The line AB is a diameter of the circle. Find the equation of the circle.
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    10. a) If the line with equation x+y = a passes through the point (3,10), then:

    3+10 = a
    a = 13

    b) (x-p)²+(y-6)²=20

    The circle must go through (3,10)

    => (3-p)² + (10-6)² = 20

    9 - 6p + p² + 16 = 20

    p² - 6p + 5 = 0

    (p-1)(p-5) = 0

    p = 1 or p = 5
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    (Original post by *girlie*)
    1) The line y=2x-8 meets the coordinate axes at A and B. The line AB is a diameter of the circle. Find the equation of the circle.
    x = 0, y = -8
    => A(0,-8)

    y = 0, x = 4
    => B(4,0)

    If AB is the diameter, the midpoint of AB will be the centre (C)

    C(2,-4)

    Length AB = √(4²+8²) = √80 = 4√5
    The radius will be half the length of the diameter
    => r = 2√5

    Eq of circle is in the form (x-a)² + (y-b)² = r² , where C(a,b)

    => (x-2)² + (y+4)² = 20
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    Thanks, mockel!
 
 
 
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Updated: June 18, 2005
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