If equation of tangent to circle {x^2} + {y^2} - 2x + 6y - 6 = 0 parallel to 3x - 4y + 7 = 0 is 3x -

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10-1.Circle and System of Circles

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If the equation of the tangent to the circle ${x^2} + {y^2} - 2x + 6y - 6 = 0$ parallel to $3x - 4y + 7 = 0$ is $3x - 4y + k = 0$, then the values of $k$ are

A

$5, -35$

B

$-5, 35$

C

$7, -32$

D

$-7, 32$

Solution

(a) Equation of circle is,

${x^2} + {y^2} – 2x + 6y – 6 = 0$

${(x – 1)^2} + {(y + 3)^2} = {(4)^2}$

Radius of circle = $4$

And centre of circle $ = (1, – 3)$

Equation of tangent $3x – 4y + k = 0$

$\frac{{3 \times 1 – 4 \times ( – 3) + k = 0}}{{\sqrt {{{(3)}^2} + {{( – 4)}^2}} }}= \pm 4$.

Hence, $k = 5, – 35$.

Standard 11

Mathematics

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