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Let each of the circles, S(1)=x^(2)+y^...

Let each of the circles,
`S_(1)=x^(2)+y^(2)+4y-1=0`,
`S_(2)=x^(2)+y^(2)+6x+y+8=0`,
`S_(3)=x^(2)+y^(2)-4x-4y-37=0`
touches the other two. Let `P_(1), P_(2), P_(3)` be the points of contact of `S_(1) and S_(2), S_(2) and S_(3), S_(3) and S_(1)` respectively and `C_(1), C_(2), C_(3)` be the centres of `S_(1), S_(2), S_(3)` respectively.
Q. The co-ordinates of `P_(1)` are :

A

(2, -1)

B

(2, 1)

C

(-2, 1)

D

(-2, -1)

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Let each of the circles, S_(1)=x^(2)+y^(2)+4y-1=0 , S_(2)=x^(2)+y^(2)+6x+y+8=0 , S_(3)=x^(2)+y^(2)-4x-4y-37=0 touches the other two. Let P_(1), P_(2), P_(3) be the points of contact of S_(1) and S_(2), S_(2) and S_(3), S_(3) and S_(1) respectively and C_(1), C_(2), C_(3) be the centres of S_(1), S_(2), S_(3) respectively. Q. The ratio ("area"(DeltaP_(1)P_(2)P_(3)))/("area"(Delta C_(1)C_(2)C_(3))) is equal to :

    A
    `3:2`
    B
    `2:5`
    C
    `5:3`
    D
    `2:3`

  • Let each of the circles, S_(1)=x^(2)+y^(2)+4y-1=0 , S_(2)=x^(2)+y^(2)+6x+y+8=0 , S_(3)=x^(2)+y^(2)-4x-4y-37=0 touches the other two. Let P_(1), P_(2), P_(3) be the points of contact of S_(1) and S_(2), S_(2) and S_(3), S_(3) and S_(1) respectively and C_(1), C_(2), C_(3) be the centres of S_(1), S_(2), S_(3) respectively. Q. P_(2) and P_(3) are image of each other with respect to line :

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

  • Let each of the circles S_(1)-=x^(2)+y^(2)+4y-1=0 S_(1)-= x^(2)+y^(2)+6x+y+8=0 S_(3)-=x^(2)+y^(2)-4x-4y-37=0 touch the other two. Also, let P_(1),P_(2) and P_(3) be the points of contact of S_(1) and S_(2) , S_(2) and S_(3) , and S_(3) , respectively, C_(1),C_(2) and C_(3) are the centres of S_(1),S_(2) and S_(3) respectively. The coordinates of P_(1) are

    A
    `(2,-1)`
    B
    `(-2,-1)`
    C
    `(-2,1)`
    D
    `(2,1)`

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