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A cat wants to catch a rat. The cat foll...

A cat wants to catch a rat. The cat follows the path whose equation is `x+y=0`. But rat follows the path whose equation is `x^(2)+y^(2)=4`. The coordinates of possible points of catching the rat are

A

`(sqrt(2), sqrt(2))`

B

`(-sqrt(2),sqrt(2))`

C

`(sqrt(2),sqrt(3))`

D

`(0,0)`

Text Solution

AI Generated Solution

To solve the problem of finding the coordinates where the cat can catch the rat, we need to find the intersection points of the two paths described by their equations. ### Step-by-Step Solution: 1. **Identify the equations of the paths**: - The cat's path is given by the equation: \[ x + y = 0 ...
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Knowledge Check

  • A dog wants to catch a cat. The dog follows the path whose equation is y-x=0 while the cat follows the path whose equation is x^(2)+y^(2)=8 . The coordinates of possible points of catching the cat are:

    A
    `(2, -2)`
    B
    `(2, 2)`
    C
    `(-2, 2)`
    D
    `(-2, -2)`

  • Separate equations of lines, whose combined equation is 4x^(2)-y^(2)+2x+y=0 are

    A
    `2x+y+1=0, 2x+y=0`
    B
    `2x-y=0,2x+y+1=0`
    C
    `x-2y+1=0,x+2y=0`
    D
    `2x-y+1=0,x-2y=0`

  • The coordinates of the point where origin is shifted is (-1,2) so that the equation 2x^(2)+y^(2)-4x+4y=0 become?

    A
    `X^(2)+2Y^(2)=6`
    B
    `2X^(2)+y^(2)=6`
    C
    `2X^(2)+Y^(2)=4`
    D
    `X^(2)+2Y^(2)=4`

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