Combined equation to the pair of tangents drawn from the origin to the circle $x^{2} + y^{2} + 4 x + 6 y + 9 = 0$ is

3 (x^{2} + y^{2}) = {(x + 2 y)}^{2}

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2 (x^{2} + y^{2}) = {(3 x + y)}^{2}

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9 (x^{2} + y^{2}) = {(2 x + 3 y)}^{2}

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x^{2} + y^{2} = {(2 x + 3 y)}^{2}

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Solution

The correct option is C $9 (x^{2} + y^{2}) = {(2 x + 3 y)}^{2}$
$S S_{1} = T^{2}$

$(x^{2} + y^{2} + 4 x + 6 y + 9) (9) = (x (0) + y (0) + 2 (x + 0) + 3 (y + 0) + 9)^{2}$

$9 (x^{2} + y^{2}) + 36 x + 54 y + 81 = (2 x + 3 y + 9)^{2}$

$9 (x^{2} + y^{2}) + 36 x + 54 y + 81 = (2 x + 3 y)^{2} + 81 + 2.9 (2 x + 3 y)$

$9 (x^{2} + y^{2}) + 36 x + 54 x y = (2 x + 3 y)^{2} + 36 x + 54 y$

$9 (x^{2} + y^{2}) = (2 x + 3 y)^{2}$

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Combined equation to the pair of tangents drawn from the origin to the circle x2+y2+4x+6y+9=0 is

The correct option is C 9(x2+y2)=(2x+3y)2SS1=T2(x2+y2+4x+6y+9)(9)=(x(0)+y(0)+2(x+0)+3(y+0)+9)29(x2+y2)+36x+54y+81=(2x+3y+9)29(x2+y2)+36x+54y+81=(2x+3y)2+81+2.9(2x+3y)9(x2+y2)+36x+54xy=(2x+3y)2+36x+54y9(x2+y2)=(2x+3y)2

Combined equation to the pair of tangents drawn from the origin to the circle $x^{2} + y^{2} + 4 x + 6 y + 9 = 0$ is