Question

Only question 12 please help.

Answer 1

For 12:
Since the line y = mx + c is a tangent, then the distance from the centre of the circle to the line is equal to the radius.

Using perpendicular distance:

`d = r = \frac -m \cdot a + 1 \cdot b - c {\sqrt{(-m)^(2) + 1}}`

`r = \fracb + am - c{\sqrt{m^(2) + 1}}`

Squaring both sides, we get:

`r^(2) = ((b - c + ma)^(2))/(m^(2) + 1)`

`(1 + m^(2))r^(2) = (b - c + ma)^(2)`, as required.