JEE Advanced2008MathematicsParabolaActual

Consider the two curves C₁: y^2=4 xC₂: x^2+y^2-6 x+1=0 , then

Options

AC₁ and C₂ touch each other only at one point
BC₁ and C₂ touch each other exactly at two points
CC₁ and C₂ intersect (but do not touch) at exactly two points
DC₁ and C₂ neither intersect nor touch each other

Correct answer

B. C₁ and C₂ touch each other exactly at two points

Step-by-step solution

For the points of intersection of the two given curves C₁: y^2=4 x and C₂: x^2+y^2-6 x+1=0 , we have aligned & x^2+4 x-6 x+1=0 & x^2-2 x+1=0 & (x-1)^2=0 & x=1,1 & y=2,-2 & aligned Thus, the given curves touch each other exactly at two points (1,2) and (1,-2) .

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