The equation of a tangent to the circle $x^{2} + y^{2} = 25$ passing through $(- 2, 11)$ is:

4 x + 3 y = 25

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7 x - 24 y = 320

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3 x + 4 y = 38

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24 x + 7 y + 125 = 0

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Solution

The correct option is A $4 x + 3 y = 25$
$(- 2, 11)$ pair is not on the circle.

$\Rightarrow y - 11 = m (x - 2)$

$y = m x + 2 m + 11$

$5 = ∣ ∣ ∣ \frac{2 m + 11}{\sqrt{1 + m^{2}}} ∣ ∣ ∣$

$25 + 25 m^{2} = 4 m^{2} + 121 + 44 m$

$21 m^{2} - 44 m - 96 = 0$

$m = \frac{- 4}{3}, \frac{24}{7}$

So, the equation of tangent is

$\Rightarrow 4 x + 3 y = 25$

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Similar questions

x^{2} + y^{2} = 25

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x^{2} + y^{2} + 13 x - 3 y = 0

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x^{2} + y^{2} + 13 x - 3 y = 0

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x^{2} + y^{2} + 13 x - 3 y = 0

2 x^{2} + 2 y^{2} + 4 x - 7 y - 25 = 0

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