Let E 1 and E 2 be two ellipses 
and 
(where a is parameter) the locus of points of intersection of the ellipses E 1 and E 2 is a set of curves
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a,d)Let P (h, k) be the point of intersection of E 1 and E 2
⇒ ⇒ 
⇒ ⇒ h 2 = a 2 (1 − − k 2 ) … (1)
and 
⇒ ⇒ k 2 = a 2 (1 − − h 2 ) … (2)
Eliminating a from (1) and (2), we get
⇒ ⇒ h 2 (1 − − h 2 ) = k 2 (1 − − k 2 )
⇒ ⇒ (h − − k) (h + k) (h 2 + k 2 − − 1) = 0
Hence the locus is a set of curves consisting of the straight lines
y = x, y = − − x and circle x 2 + y 2 = 1.
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