Which of following lines is a tangent to circle {x^2} + {y^2} = 25 for all values of m .....

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10-1.Circle and System of Circles

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Which of the following lines is a tangent to the circle ${x^2} + {y^2} = 25$ for all values of $m$.....

A

$y = mx + 25\sqrt {1 + {m^2}} $

B

$y = mx + 5\sqrt {1 + {m^2}} $

C

$y = mx + 25\sqrt {1 - {m^2}} $

D

$y = mx + 5\sqrt {1 - {m^2}} $

Solution

(b) Line $y = mx + c$ is a tangent if

$c = \pm a\sqrt {1 + {m^2}} $

$\therefore $$y = mx + 5\sqrt {1 + {m^2}} $.

Standard 11

Mathematics

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