Mathematics Question and Solution
Let the centre of the circle be N
Therefore;
N coordinate is;
N(2, 4).
Point P is;
P(-2, (17/2))
Point Q is;
Q(x, 0)
Gradient of length NP is;
(4-(17/2))/(2+2)
= -9/8
Notice;
Length PQ is a tangent to length NP.
Therefore length PQ gradient is;
-1/length NP gradient
= -1/(-9/8)
PQ gradient = 8/9
Calculating x coordinate at point Q.
(0-(17/2))/(x+2) = 8/9
-153/2 = 8x + 16
16x + 32 = -152
16x = -185
x = - 185/16
Therefore;
Area green exactly in square units is;
½((2, 4) (-2, (17/2)) ((-185/16), 0) (2, 4))
= ½(800+3145-1480)/32
= ½(3945-1480)/32
= 2465/64 square units.
