Line y = x + c will intersect circle {x^2} + {y^2} = 1 in two coincident points, if

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10-1.Circle and System of Circles

easy

The line $y = x + c$will intersect the circle ${x^2} + {y^2} = 1$ in two coincident points, if

A

$c = \sqrt 2 $

B

$c = - \sqrt 2 $

C

$c = \pm \sqrt 2 $

D

None of these

Solution

(c) $y = x + c$ intersects at two coincident points,

$i.e.$ it is a tangent, therefore ${c^2} = 1(1 + 1) $

$\Rightarrow c = \pm \sqrt 2 $.

Standard 11

Mathematics

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