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in Mathematics by (53.1k points)

If the circle x2 + y2 = a2 cuts the hyperbola xy = c2 at four points (xk, yk) (where k = 1, 2, 3 and 4), then

(a)  x1 + x2 + x3 + x4 = 0

(b)  y1 + y2 + y3 + y4 = 0

(c)  x1 x2 x3 x4 = c4

(d)  y1 y2 y3 y4  = c4

1 Answer

+1 vote
by (53.3k points)
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Best answer

Correct option  (a)(b)(c)(d)

Explanation :

The abscissa xk (where k = 1, 2, 3 and 4) are the roots of the equation x2 + c4/x2 = a4

⇒ x4 - a2x2 + c4 = 0

Therefore
x1 + x2 + x3 + x4 = 0
Since the coefficient of x3 is zero, we have

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