Question
Question: If the circle x<sup>2</sup> + y<sup>2</sup> = a<sup>2</sup> intersects the hyperbola xy = c<sup>2</s...
If the circle x2 + y2 = a2 intersects the hyperbola xy = c2 in four points P (x1, y1), Q(x2, y2) R(x3, y3), S(x4, y4) then
A
x1 + x2 + x3 + x4 = 0
B
y1 + y2 + y3 + y4 = 0
C
x1x2x3x4 = c4
D
y1y2y3y4 = c4
Answer
y1y2y3y4 = c4
Explanation
Solution
Solving given equation we have x2 + x2c4=a2
⇒ x4 - a2x2 + c4 = 0.
∴ Σx1 = x1 + x2 + x3 + x4 = 0 and x1x2x3x4 = c4
Replacing x by y, we get Σy1 = 0 and y1y2y3y4 = c4.