\(
\eqalign{
& 19. \cr
& (x - 7)^2 + (y - 9)^2 = 100 \cr
& \downarrow y = - {3 \over 4}x + 17{3 \over 4} \cr
& (x - 7)^2 + \left( { - {3 \over 4}x + 17{3 \over 4} - 9} \right)^2 = 100 \cr
& (x - 7)^2 + \left( { - {3 \over 4}x + 8{3 \over 4}} \right)^2 = 100 \cr
& (x - 7)^2 + {{\left( { - 3x + 35} \right)^2 } \over {4^2 }} = 100 \cr
& 16(x - 7)^2 + \left( { - 3x + 35} \right)^2 = 1600 \cr
& 16x^2 - 224x + 784 + 9x^2 - 210x + 1225 = 1600 \cr
& 25x^2 - 434x + 409 = 0 \cr
& \downarrow GR \cr
& x = 1 \vee x = 16{9 \over {25}} \cr
& \downarrow GR \cr
& \left\{ \matrix{
x = 16{9 \over {25}} \hfill \cr
y = - {3 \over 4} \cdot 16{9 \over {25}} + 17{3 \over 4} = 5{{12} \over {25}} \hfill \cr} \right. \cr
& Q\left( {16{9 \over {25}},5{{12} \over {25}}} \right) \cr}
\)
