﻿ Consider the two curves C1 : y2 = 4x ; C2 : x2 + y2 – 6x + 1, then  : Kaysons Education

# Consider The Two Curves C1 : y2 = 4x ; C2 : x2 + y2 – 6x + 1, Then

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## Question

### Solution

Correct option is

C1 and C2 touch each other exactly at two points

Solving the two equations, we get

x2 + 4x – 6x + 1 = 0

⇒        x2 + 2x + 1 = 0

⇒        = 1 and y = ±2

So the two curve meet at two points (1, 2) and (1, –2). Equation of tangents at (1, 2) to C1is y(2) = 2 (x + 1)

⇒        y = x +1

and equation of the tangent at (1, 2) to C2 is

x. 1 + y(2) – 3(+ 1) + 1 = 0  ⇒ y = x + 1

Showing that C1­ and C2 have a common tangent at the point (1, 2).

Similarly they have a common tangent

y = –(x + 1) at (1, –2)

Hence the two curve touch each other exactly at two points.

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