#Equation of a tangent to circles

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young scroll
#

C is a circle with centre (0,0)
L is a straight line with a negative gradient.
The circle C and the line L intersect at the points A and B.
The coordinates of A are (-9,2)
The x coordinate of B is 7
Find the equation of line L

celest mural
#

x^2 + y^2 = r^2
(-9)^2 + 2^2 = r^2 = 85 <=> r = root85
using distance formula from centre to point B
(7)^2 + (y)^2 = 85
y^2 = 36
y = +-6 so B is either (7,6) or (7,-6) so we can find gradient of AB
using first B
6-2/7--9 is +ve so B isnt (7,6) and must be (7,-6)
so gradient using that B is -6-2/7--9=-1/2
so equation of L is y+6 = -1/2 * (x-7)
y = -x/2 - 5/2