(D) The power of a point $(x_1, y_1)$ with respect to a circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by $x_1^2 + y_1^2 + 2gx_1 + 2fy_1 + c$. Given

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(D) The power of a point $(x_1, y_1)$ with respect to a circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by $x_1^2 + y_1^2 + 2gx_1 + 2fy_1 + c$. Given the circle equation $x^2 + y^2 + 4x - 6y - a = 0$ and the point $(1, 6)$,the power is $-16$. Substituting the point $(1, 6)$ into the circle equation: $(1)^2 + (6)^2 + 4(1) - 6(6) - a = -16$ $1 + 36 + 4 - 36 - a = -16$ $5 - a = -16$ $a = 5 + 16$ $a = 21$

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

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The value of $a$,such that the power of the point $(1, 6)$ with respect to the circle $x^2 + y^2 + 4x - 6y - a = 0$ is $-16$,is

TS EAMCET 2015 All TS EAMCET

A
$7$
B
$11$
C
$13$
D
$21$

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10-1.Circle and System of Circles

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Geometrical problems regarding circle and its properties

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TS EAMCET 2015 Paper All TS EAMCET years →

Find the equation of the diameter of the circle $x^2 + y^2 - 4x + 2y - 11 = 0$ which corresponds to the system of parallel chords $x - 2y + c = 0$.

Medium

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Match the statements in Column $I$ with the properties in Column $II$.

Column $I$ Column $II$

$(A)$ Two intersecting circles $(p)$ have a common tangent

$(B)$ Two mutually external circles $(q)$ have a common normal

$(C)$ Two circles,one strictly inside the other $(r)$ do not have a common tangent

$(D)$ Two branches of a hyperbola $(s)$ do not have a common normal

DifficultIIT 2007

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$A$ circle with radius $12$ lies in the first quadrant and touches both the axes. Another circle has its centre at $(8, 9)$ and radius $7$. Which of the following statements is true?

Medium

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The equation of the chord of the circle $x^2+y^2-4x=0$ whose midpoint is $(1,0)$ is

EasyWBJEE 2009

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Three circles of radii $1, 2$ and $3$ units respectively touch each other externally in the plane. The circumradius of the triangle formed by joining the centers of the circles is

KVPY 2016

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Column $I$	Column $II$
$(A)$ Two intersecting circles	$(p)$ have a common tangent
$(B)$ Two mutually external circles	$(q)$ have a common normal
$(C)$ Two circles,one strictly inside the other	$(r)$ do not have a common tangent
$(D)$ Two branches of a hyperbola	$(s)$ do not have a common normal

The value of $a$,such that the power of the point $(1, 6)$ with respect to the circle $x^2 + y^2 + 4x - 6y - a = 0$ is $-16$,is

Similar Questions

Find the equation of the diameter of the circle $x^2 + y^2 - 4x + 2y - 11 = 0$ which corresponds to the system of parallel chords $x - 2y + c = 0$.

$A$ circle with radius $12$ lies in the first quadrant and touches both the axes. Another circle has its centre at $(8, 9)$ and radius $7$. Which of the following statements is true?

The equation of the chord of the circle $x^2+y^2-4x=0$ whose midpoint is $(1,0)$ is

Three circles of radii $1, 2$ and $3$ units respectively touch each other externally in the plane. The circumradius of the triangle formed by joining the centers of the circles is

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