The shortest distance from the line $3 x + 4 y = 25$ to the circle $x^{2} + y^{2} = 6 x - 8 y$ is equal to

7 / 5

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9 / 5

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11 / 5

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32 / 5

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Solution

The correct option is A $7 / 5$

$\begin{matrix} x^{2} + y^{2} - 6 x + 8 y = 0 {(x - 3)}^{2} + {(y + y)}^{2} = 25 3 x + 4 y - 25 = 0 S h o r t e s t d i s tan c e, d = \frac{| 3 (3) + 4 (- 4) - 25 |}{5} - 5 = \frac{31 - 25}{5} = \frac{7}{5} H e n c e, o p t i o n A i s t h e c o r r e c t a n s w e r . \end{matrix}$

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Similar questions

x^{2} + y^{2} - 6 x + 8 y = 0

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