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Only question 12 please help.

Only question 12 please help.-example-1
User TreyE
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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.
User Ceridan
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