The power of P(1,2) with respect to the circle $x^{2} + y^{2} + 4 x + 2 y + 3$ = 0 is double the power of P with respect to $x^{2} + y^{2} + 2 x + y + k$ = 0 then the value of k is

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Solution

The correct option is C
-1

P(1,2)
$x^{2} + y^{2} + 4 x + 2 y + 3$ = 0
$S_{11}$ = $1 + 4 + 4 + 4 + 3$
$S_{11}$ = 8
For $x^{2} + y^{2} + 2 x + y + k$ = 0
$S_{11}$ = $1 + 4 + 2 + 2 + k$ = 9+k
$∴$ 2(9+k)=16
$k$ = $8 - 9$ = $- 1$

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The power of P(1,2) with respect to the circle x2+y2+4x+2y+3 = 0 is double the power of P with respect to x2+y2+2x+y+k = 0 then the value of k is

The correct option is C -1 P(1,2) x2+y2+4x+2y+3 = 0 S11 = 1+4+4+4+3 S11 = 8 For x2+y2+2x+y+k = 0 S11= 1+4+2+2+k = 9+k ∴ 2(9+k)=16 k = 8−9 = −1

The power of P(1,2) with respect to the circle $x^{2} + y^{2} + 4 x + 2 y + 3$ = 0 is double the power of P with respect to $x^{2} + y^{2} + 2 x + y + k$ = 0 then the value of k is

The correct option is C
-1

P(1,2)
$x^{2} + y^{2} + 4 x + 2 y + 3$ = 0
$S_{11}$ = $1 + 4 + 4 + 4 + 3$
$S_{11}$ = 8
For $x^{2} + y^{2} + 2 x + y + k$ = 0
$S_{11}$ = $1 + 4 + 2 + 2 + k$ = 9+k
$∴$ 2(9+k)=16
$k$ = $8 - 9$ = $- 1$