CircleHard
Question
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
Options
A.x1 + x2 + x3 + x4 =0
B.y1 + y2 + y3 + y4 = 0
C.x1x2x3x4 = C4
D.y1y2y3y4 = C4
Solution
It is given that
x2 + y2 = a2 .....(i)
and xy = c2 .....(ii)
We obtain x2 + c2 / x2 = a2
⇒ x4 - a2x2 + c4 = 0
Now, x1, x2, x3, x4, will be roots of Eq. (iii)
Therefore, ∑ x1 = x2 + x3 + x3 + x4 = 0
and product of the roots
x1x2x3x4 = c4
Similarl y, y1 + y2 + y3 + y4 = 0 and y1y2y3y4 = c4
Hence, all options are correct.
x2 + y2 = a2 .....(i)
and xy = c2 .....(ii)
We obtain x2 + c2 / x2 = a2
⇒ x4 - a2x2 + c4 = 0
Now, x1, x2, x3, x4, will be roots of Eq. (iii)
Therefore, ∑ x1 = x2 + x3 + x3 + x4 = 0
and product of the roots
x1x2x3x4 = c4
Similarl y, y1 + y2 + y3 + y4 = 0 and y1y2y3y4 = c4
Hence, all options are correct.
Create a free account to view solution
View Solution FreeMore Circle Questions
From a point P tangent is drawn to the circle x2 + y2 = a2 and a tangent is drawn to x2 + y2 = b2. If these tangent are ...If least numerical value of slope of line which is tangent to hyperbola = 1 is , a ∈ R0 is obtained at a = k. For ...The radius of the circle passing through the points (1, 2), (5, 2) & (5, - 2) is:...The length of the diameter of the circle whichtouches the x-axis at the point (1, 0) and passesthrough the point (2, 3) ...If (4, 3) and (−12, −1) are end points of a diameter of a circle, then the equation of the circle is-...