Question

Show that the line with equation 4y+3x=44 is a tangent to the circle with centre (5,1) and radius 5.

Answer 1

When a line is a tangent to a circle then the point of a tangent on a circle is perpendicular and also equal to the radius

So for perpendicular.

                                            $P = \frac{ax+by+c}{\sqrt{a^2 + b^2} }$

4y + 3x - 44 = 0

So, a = 4

      b = 3

      c = -44

      x = 5

      y = 1

Putting the values in the formula, we get

P = -4.2

Since the radius of the circle 5 is not equal  to P, The line is not a tangent to the circle.