The equation of the circle concentric with the circle x 2- y 2-8 x -6 y -5-0 and passing through the point -2-7 is A- x2-y2-8 x-6 y-30-0B- x2-y2-8 x-6 y-26-0C- x2-y2-8 x-6 y-27-0D- x2-y2-8 x-6 y-0

The correct option is C x^2+y^2 8x+6y 27=0Given circle : nbsp; x^2+y^2 8x+6y 5=0 nbsp; Any concentric circle is written as nbsp; x^2+y^2 8x+6y+k=0 Above ...

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Standard XII

Mathematics

Definition of Circle

The equation ...

Question

The equation of the circle concentric with the circle $x^{2} + y^{2} - 8 x + 6 y - 5 = 0$ and passing through the point $(- 2, - 7)$ is

x^{2} + y^{2} - 8 x + 6 y - 30 = 0

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x^{2} + y^{2} - 8 x + 6 y - 26 = 0

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x^{2} + y^{2} - 8 x + 6 y - 27 = 0

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x^{2} + y^{2} - 8 x + 6 y = 0

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Solution

The correct option is C $x^{2} + y^{2} - 8 x + 6 y - 27 = 0$
Given circle :
$x^{2} + y^{2} - 8 x + 6 y - 5 = 0$
Any concentric circle is written as
$x^{2} + y^{2} - 8 x + 6 y + k = 0$
Above circle passes through $(- 2, - 7)$
$∴ 4 + 49 + 16 - 42 + k = 0$
$\Rightarrow k = - 27$
$∴$ Equation of circle is
$x^{2} + y^{2} - 8 x + 6 y - 27 = 0$

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is-

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The equation of the circle concentric with the circle x2+y2−8x+6y−5=0 and passing through the point (−2,−7) is

The correct option is C x2+y2−8x+6y−27=0Given circle : x2+y2−8x+6y−5=0 Any concentric circle is written as x2+y2−8x+6y+k=0 Above circle passes through (−2,−7) ∴4+49+16−42+k=0 ⇒k=−27 ∴ Equation of circle is x2+y2−8x+6y−27=0

The equation of the circle concentric with the circle $x^{2} + y^{2} - 8 x + 6 y - 5 = 0$ and passing through the point $(- 2, - 7)$ is