IIT-JEE 2008 · Paper 1 · Mathematics Q1

MathematicsSingle correct+3 / -1Question 1 of 69

Consider the two curves
$C_1:y^2=4x,\qquad C_2:x^2+y^2-6x+1=0.$
Then,

C_1

and

C_2

touch each other only at one point

C_1

and

C_2

touch each other exactly at two points

C_1

and

C_2

intersect (but do not touch) at exactly two points

C_1

and

C_2

neither intersect nor touch each other

Answer and worked solution

Official answer: B

Intersect. Put $y^2=4x$ into the circle:
$x^2+4x-6x+1=0\implies(x-1)^2=0.$
The only common abscissa is the double root $x=1$ , giving $y=\pm2$ .

Touching. A double root means the curves meet tangentially, at the two points $(1,2)$ and $(1,-2)$ .

(B)

Topics:Parabola Equation of a circle

IIT-JEE 2008 · Paper 1, Mathematics question 1