Question
Mathematics Question on limits and derivatives
Directions: The following question has four choices, out of which one or more are correct.The equations of two ellipses are x2p2+y2=1 and x2+y2p2=1,=1, where p is a parameter. The locus of the points of intersection of both the ellipses is a set of curves comprising
A
(A) two straight lines
B
(B) one straight line
C
(C) one circle
D
(D) one parabola
Answer
(A) two straight lines
Explanation
Solution
Explanation:
Let the point of intersections is (h,k). Therefore,h2p2+k2=1 and h2+k2p2=1h2p2=1−k2 and 1−h2=k2p2h21−k2=p2 and p2=k21−h2h21−k2=k21−h2h2(1−h2)=k2(1−k2)h2−h4=k2−k4h2−k2−(h4−k4)=0(h2−k2)−(h2−k2)(h2+k2)=0(h2−k2)[1−(h2+k2)]=0h2=k2Orh2+k2=1x2=y2Orx2+y2=1x=±yOrx2+y2=1Hence, it is the required solution.x=±y represents two straight linesx2+y2=1 represents a circle