QJEEAdv08Mae012: JEE Advanced 2008 Mathematics - Class 11 JEEAdv08Mae012 Solution: Consider the two curves C 1 : y 2 = 4 x , C 2 : x 2 + y 2 − 6 x …

Question

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Consider the two curves

C_{1} : y^{2} = 4 x, C_{2} : x^{2} + y^{2} - 6 x + 1 = 0

. Then,

Accepted Answer

Given that,

$C_{1} : y^{2} = 4 x$

$C^{2} : x^{2} + y^{2} - 6 x + 1 = 0$

Putting $y^{2} = 4 x$ in $x^{2} + y^{2} - 6 x + 1 = 0$ , we get

$x^{2} + 4 x - 6 x + 1 = 0 \Rightarrow (x - 1)^{2} = 0$

$x = 1$

putting $x = 1$ in $y^{2} = 4 x$ we get $y = \pm 2$

IIT-JEE 2008 Paper 1 Offline Mathematics - Ellipse Question 9 English Explanation

So, the curves touches each other at two points (1, 2) and (1, $-$ 2),

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