Question

Find the equation of the normal to the circle $x^2+y^2=5$ at the point $(1,2)$.

Answer 1

Since the tangent is perpendicular to the radius

of the circle at the point (1,2) the normal, which is

$\perp$ lag to the tangent must be $\parallel$ el to the radius

So we need gradient, since we have given fixed point

(1,2) with center (0,0)

gradient (slope of the normal is ) $=\frac{1-0}{2-0}=\frac{1}{2}$

equation of normal $\Rightarrow y-y_1=m(x-x_1)$

$(y-1)=\frac{1}{2}(x-2)$

$2y-2=x-2$

$2y=x$

$y=\frac{1}{2}x$