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Circles are drawn touching the co-ordina...

Circles are drawn touching the co-ordinate axis and having radius 2, then

A

Centre of these circles lie on the pair of lines `y^(2) – x^(2) = 0`

B

centre of these circles lie only on the line y = x

C

Area of the quadrilateral whose vertices are centre of these circles is 16 sq. units.

D

Area of the circle touching these four circles internally is `4pi(3 + 2sqrt(2))`

Text Solution

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The correct Answer is:
A, C, D
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Knowledge Check

  • Let P(alpha,beta) be a point in the first quadrant. Circles are drawn through P touching the coordinate axes. Radius of one of the circles is

    A
    `(sqrt(a)-sqrt(beta))^(2)`
    B
    `(sqrt(alpha)+sqrt(beta))^(2)`
    C
    `alpha +beta -sqrt(alpha beta)`
    D
    `alpha +beta -sqrt(2alpha beta)`

  • The equation of the circle in the third quadrant touching each co-ordinate axis at a distance of 2 units from the origin is

    A
    `(X-2)^(2) + (y-2)^(2) = (2)^(2)`
    B
    `(x+2)^(2) + (y+2)^(2) = 4`
    C
    `(x+2)^(2) + (y+2)^(2) = 2`
    D
    `(x-2)^(2) + (y-2)^(2) = 2`

  • The equation of the circle in the first quadrant touching each co-ordinate axis at a distance of one unit from the origing is :

    A
    `x^(2) + y^(2) - 2x - 2y + 1 = 0 `
    B
    `x^(2) + y^(2) - 2x - 2y - 1 = 0 `
    C
    `x^(2) + y^(2) - 2x - 2y = 0 `
    D
    `x^(2) + y^(2) - 2x + 2y - 1 = 0 `

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