1. (a) If a chord of the parabola y^2 = 4ax is a normal at one of its ends, show that its mid-point lies on the curve 2(x − 2a) = y^2/a + 8a^3/y^2
.
Prove that the shortest length of such a chord is 6a√3.
(b) Find the asymptotes of the hyperbola
x^2 − y^2 + 2x + y + 9 = 0.
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Expert's answer
2020-07-02T19:04:54-0400
If the normal at the point
P(at12,2at1) meets the parabola y2=4ax again at Q(at22,2at2) then
b) A hyperbola with a horizontal transverse axis and center at (h, k) has one asymptote with equation y = k + a(x - h) and the other with equation y = k - a(x - h).a = distance from vertices to the centery=233233(x−(−1))+21,y=−233233(x−(−1))+21
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