Question

Thetangent line to a circle may be defined as the line that intersectsin a single point, called the point of tangency. See thefigure.

If the equation of the circle is x²+y² =r² and the equation of the tangent line is y = mx+b,show that:

a) r² (1+m²) = b² [Thequadratic equation x² + (mx + b)² =r² has exactly one solution.

b) The point of tangency is (-r²m/b ,r²/b)

c) The tangent line is perpendicular to the line containing thecenter of the circle and the point of tangency.

The tangent line to a circle may be defined as the line that intersects in a single point, called the point of tangency. See the figure. If the equation of the circle is x^2+y^2 = r^2 and the equation of the tangent line is y = mx+b, show that: a) r^2 (1+m^2) = b^2

Show transcribed image text The tangent line to a circle may be defined as the line that intersects in a single point, called the point of tangency. See the figure. If the equation of the circle is x^2+y^2 = r^2 and the equation of the tangent line is y = mx+b, show that: a) r^2 (1+m^2) = b^2