Question

1. (a) If a chord of the parabola y 2 = 4ax is a normal at...

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(xx 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
2y
2 + 2x + y + 9 = 0.

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