Question

The equation of tangent with slope m of the circle $x^2+y^2=a^2$ are given by $y=mx\pm m\sqrt{1+a^2}$

• A. True
• B. False

Answer 1

The correct option is B

False

We want to find the equation of the tangent whose slope is m. the equation given to us is of the form y

=mx+c. we have to check if c=$\pm m\sqrt{1+a^2}$

Let the equation of the circle be y=mx+c

We know the perpendicular from center to the tangent is equal to radius.

(we will be using this condition in solving problem related to tangents)

$\Rightarrow$ Distance of (0,0) from mx-y+c=0,=4

$\Rightarrow \left|\frac{c}{\sqrt{1+m^2}}\right|=a$

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

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

$\Rightarrow$ The given statement is wrong