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    CAT Concentric Circle - Practice Questions & MCQ

    Edited By admin | Updated on Oct 04, 2023 04:20 PM | #CAT

    Quick Facts

    • 6 Questions around this concept.

    Solve by difficulty

    QuestionMEDIUM

    The equation of a circle concentric with x^2+y^2=4 and having a radius of 8 units is:

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    Equation of the circle which is concentric with x^2+y^2-4x-4y+16=0 and having radius 6 units is:

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    Which of the following are concentric circle:

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    Two circles or more than that are said to be concentric if they have the same centre but different radii. (True/False)

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    These two general equations of the circle  \mathrm{x^2+y^2+2gx+2fy+c=0}  and \mathrm{x^2+y^2+2gx+2fy+c'=0} are concentric with each other. (True/False)

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    Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is tangent to C2, then the diameter, in cm, of C1 is:

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    Concepts Covered - 1

    Concentric Circle

    Two circles or more than that are said to be concentric if they have the same centre but different radii.

    Let S1 is equation of circle with radius r1 and S2 is equation of another circle with radius r2​.

    \\\mathrm{S_{1}=(x-h)^{2}+(y-k)^{2}=r_{1}^{2}} \\\\ \mathrm{S_{2}=(x-h)^{2}+(y-k)^{2}=r_{2}^{2}}

    where, \\\mathrm{r_1\neq r_2}

    Also, 

    As we know that the general equation of the circle is \mathrm{x^2+y^2+2gx+2fy+c=0} having centre at (- g, - f) and radius =\sqrt{\mathrm{g}^{2}+\mathrm{f}^{2}-\mathrm{c}}.

    Therefore, the equation of a circle concentric with the given circle \mathrm{x^2+y^2+2gx+2fy+c=0}  is \mathrm{x^2+y^2+2gx+2fy+c'=0}.

    Both the circle have the same centre (- g, - f) but their radii are not equal (since, c ≠ c').

    Study other Related Concepts

    CAT Concentric Circle Current Topic

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