[[EDT]AmanSingh123]

The point C lies on line 1 and has x co ordinates equal to p
The lenght of AC is 5 units
Show that p satisfies p2 - 4p - 16 = 0


line 1 is y=-1/2x + 6
co ordinates of b is (-2, 7)
co ordinates of a is (2, 5)

[donB]

Well, its really easy.

You got the slope of the line, which is -0.5.
Now, using the slope and the two equations obtained from the slopes of AC & CB, find y.
Substitute y in the distance ,(= 5), equation in terms of 'p'.
Solve the equation to obtain the relation.