Question

Find the equations of the tangents to the circle x² +y² = 9 which make an angle of 60° with the axis.

Answer 1

Since tangents make an angle of 60° with the x–axis so slope of tangent

m = tan60°=m= √3

radius of circle x² +y² = 9 is 3

we know equation of tangent to a circle x² +y² = a² is

y = mx ± a \(\sqrt{1+ m^2}\)

\(∴ y = \sqrt{3}\, x ± 3 \sqrt{1+ 3}\)

= √3 x ± 6

or √3 x–y ± 6 = 0 ie., √3 x–y+6 = 0 and √3 x–y–6 =0 are equations of tangents