the point H is a variable point on the cyrve x^2-y^2=8. The feet of perpendicular from H to the x-axis and y-axis are M and N respectively.
Find the equation of locus the mid-point of MN.
locus(3)
2011-04-20 4:51 am
回答 (1)
2011-04-20 6:52 am
✔ 最佳答案
Let H be (h, k), so h^2 - k^2 = 8.............(1)M is (h, 0) and N is (0, k).
Mid point of MN is (h/2, k/2)
That is x = h/2 and y = k/2.
From (1), (2x)^2 - (2k)^2 = 8
4x^2 - 4y^2 = 8
x^2 - y^2 = 2 is the locus.
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