(B) The equation of the circle is $x^2 + y^2 = 25$,which is of the form $x^2 + y^2 = a^2$,where $a = 5$.The condition for the line $y = mx + c$ to be

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(B) The equation of the circle is $x^2 + y^2 = 25$,which is of the form $x^2 + y^2 = a^2$,where $a = 5$.The condition for the line $y = mx + c$ to be a tangent to the circle $x^2 + y^2 = a^2$ is $c = \pm a\sqrt{1 + m^2}$.Substituting $a = 5$,we get $c = \pm 5\sqrt{1 + m^2}$.Thus,the equation of the tangent is $y = mx \pm 5\sqrt{1 + m^2}$.Comparing this with the given options,the correct line is $y = mx + 5\sqrt{1 + m^2}$.

Class 11 Mathematics 1 Conic Sections: Circle Tangent and normal to a circle

Medium

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

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1 Conic Sections: Circle

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Tangent and normal to a circle

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

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