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10-1.Circle and System of Circles
easy
The equations of the tangents to circle $5{x^2} + 5{y^2} = 1$, parallel to line $3x + 4y = 1$ are
A
$3x + 4y = \pm 2\sqrt 5 $
B
$6x + 8y = \pm \sqrt 5 $
C
$3x + 4y = \pm \sqrt 5 $
D
None of these
Solution
(c) Equation of tangent $y = \frac{{ – 3}}{4}x \pm \frac{1}{{\sqrt 5 }}\sqrt {1 + {{\left( {\frac{{ – 3}}{4}} \right)}^2}} $
==> $y = \frac{{ – 3}}{4}x \pm \frac{1}{{\sqrt 5 }}\sqrt {\frac{{16 + 9}}{{16}}} $
==> $4y = – 3x \pm \sqrt 5$
$\Rightarrow 3x + 4y = \pm \sqrt 5 $
Standard 11
Mathematics
