consider the two curves

IIT QUESTION QUERY

CONSIDER THE TWO CURVES

C1: Y² =4X

C2: X² + Y²-6X+1=0

THEN,

(A) C1 AND C2 TOUCH EACH OTHER ONLY AT ONE POINT

(B) C1 AND C2 TOUCH EACH OTHER EXACTLY AT TWO POINTS

(C) C1 AND C2 INTERSECT (BUT DO NOT TOUCH ) AT EXACTLY TWO POINTS

(D) C1 AND C2 NIETHER INTERSECT NOR TOUCH EACH OTHER

u shud have written the question be4

substitute y^2=4x in the 2nd equation

u get (x-1)^2=0

imply there r 2 roots but equal

so, the lines do not intersect but touch at 2points i.e.. (1,4) &(1,4)

 

The curves C₁,C₂ intersect at points given by x²+4x-6x+1=0x=1.

Hence,y²=4 or y=2,-2.So,the curves intersect each other in two points (1,2) and (1,-2).Thus,the ans is (C).