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JEE Advanced 2008Paper 1
Exam
JEE Advanced
Year
2008
Paper
Paper 1
Subject
Mathematics
Chapter
Parabola

JEE Advanced 2008 · Paper 1 · Mathematics · Parabola

Consider the two curves C_1: y^2=4 x C_2: x^2+y^2-6 x+1=0 , then

Consider the two curves C1:y2=4xC_1: y^2=4 x C2:x2+y2−6x+1=0C_2: x^2+y^2-6 x+1=0, thenConsider the two curves C_1: y^2=4 x C_2: x^2+y^2-6 x+1=0 , thenConsider the two curves C_1: y^2=4 x C_2: x^2+y^2-6 x+1=0 , then

Options

  1. AC1C_1 and C2C_2 touch each other only at one point
  2. BC1C_1 and C2C_2 touch each other exactly at two points
  3. CC1C_1 and C2C_2 intersect (but do not touch) at exactly two points
  4. DC1C_1 and C2C_2 neither intersect nor touch each other

Correct answer

B. C1C_1 and C2C_2 touch each other exactly at two points

Step-by-step solution

Consider the two curves C_1: y^2=4 x C_2: x^2+y^2-6 x+1=0 , then
For the points of intersection of the two given curves C_1: y²=4 x \text{ and }C_2: x²+y²-6 x+1=0 , \text{, }we have x2+4x−6x+1=0⇒x2−2x+1=0⇒(x−1)2=0⇒x=1,1⇒y=2,−2\begin{aligned}& x²+4 x-6 x+1=0 \\ & \Rightarrow \quad x²-2 x+1=0 \\ & \Rightarrow \quad(x-1)^2=0 \\ & \Rightarrow \quad x=1,1 \\ & \Rightarrow \quad y=2,-2 \\ & \end{aligned}Thus,$ the given curves touch each other exactly at two points(1,2) and (1,-2).
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