Question

Draw the unit circle with center (0,0)and plot the point P=(6,2). Observe there are TWO lines tangent to the circle passing through the point P.
1)the tangent line on top of the circle(L1) has coordinates?

a) what is the equation for L1?

2) the tangent line below the circle(L2) has coordinates?

b)what is the equation for L2?

Answer 1

Answer:

Step-by-step explanation:

Given that a tangent is drawn from P (6,2) to unit circle with center at the origin.

The tangent passing through (6,2) would have equaiton of the form

$y-6 = m(x-2)\\y =mx-2m+6$ for suitable m.

Because this line is tangent, distance of centre of circle namely origin is the radius 1.

i.e. $|\frac{-2m+6}{\sqrt{1+m^2} } |=1\\(-2m+6 )^2 = 1+m^2\\3m^2-24m+35=0\\\\m=1.918, 6.082$

the coordinates are the intersection of the tangent with the circle

They are (-0.162, 0.987) and (0.462,-0.887)