The equation of the tangent to the circle x^2 | vedclass

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(D) The given circle is $x^2 + y^2 - 2x - 4y - 4 = 0$. Comparing with $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -1$,$f = -2$,and $c = -4$. The cente

Vedclass · Accepted Answer

$4x + 3y - 25 = 0$

Vedclass · Answer

(D) The given circle is $x^2 + y^2 - 2x - 4y - 4 = 0$. Comparing with $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -1$,$f = -2$,and $c = -4$. The center is $(1, 2)$ and the radius $r = \sqrt{g^2 + f^2 - c} = \sqrt{1 + 4 + 4} = 3$.The line perpendicular to $3x - 4y - 1 = 0$ is of the form $4x + 3y + k = 0$.The perpendicular distance from the center $(1, 2)$ to the tangent $4x + 3y + k = 0$ must be equal to the radius $r = 3$.Using the distance formula: $\frac{|4(1) + 3(2) + k|}{\sqrt{4^2 + 3^2}} = 3$.$\frac{|4 + 6 + k|}{5} = 3 \implies |10 + k| = 15$.This gives $10 + k = 15$ or $10 + k = -15$.So,$k = 5$ or $k = -25$.The possible tangents are $4x + 3y + 5 = 0$ and $4x + 3y - 25 = 0$. Comparing with the options,the correct answer is $4x + 3y - 25 = 0$.

The equation of the tangent to the circle $x^2 + y^2 - 2x - 4y - 4 = 0$ which is perpendicular to $3x - 4y - 1 = 0$ is:

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