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Math Help - analytic geometry

  1. #1
    Newbie
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    analytic geometry

    somebody else help me in solving these problems. thanks

    1. Find the distance between the lines 3x+y-12=0 and 3x+y=0.
    2. what is the center of an ellipse 64x^2 + 25y^3=1600?
    3. Determine the coordinates of the point which is 3/5 of the way from the point (3,5) to the point (-3,5).
    4. Find the minor axis of an ellipse x^3 9y^29.
    5. Given the equation of the directrix of the curve 3x=2y^2-4y7.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Please post your working.
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  3. #3
    Junior Member
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    Smile

    For the first one - draw the pair of \\ lines on graph paper. One goes through the origin. Now construct a right angled triangle that has one point at the origin, one point on the positive x axis and the other on the uppermost line you plotted (the right angle should be the bottom right corner of the triangle). You now want to calculate the hypotenuse of this triangle. You can do this by constructing a formula for the line through the hypotenuse - it needs to be of the form y=ax where a is the gradient which is perpendicular to the gradients you already have (hint: reciprocal). Now find the intersection of your constructed line with the uppermost \\ line. Solving for x and y will give you the needed values for two edges of the right angle triangle - now use pythag!

    Now you can do the working

    HTH

    Si
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