己知下列聯立方程的圖像有一個交點P.

己知下列聯立方程的圖像有一個交點P.
求
(a). k;
(b) P點的座標
y=2x2
y=6kx-9
將 y = 6kx-9 代入 y = 2x2
得
2x2 = 6kx – 9
2x2 – 6kx + 9 = 0
因只有一個交點，所以它的判別式為零
B2 – 4AC = 0
(–6k) 2 – 4(2)(9) = 0
36k2 – 72 = 0
k2 = 2
k = ±√2
若 k = √2
2x2 – 6(√2)x + 9 = 0
x = 2.121
y = 2x2 = 2(2.121)2
y = 9
P 的坐標為 (2.121,9)
若 k = -√2
2x2 + 6(√2)x + 9 = 0
x = -2.121
y = 2x2 = 2(-2.121)2
y = 9
P 的坐標為 (-2.121,9)

(a)
2x^2=6kx-9
9=6kx-2x^2
9=2x(3k-x)
3k-x=9/2x
3k=(9/2x)+x
3k=(11/2)x
k=(11/6)x
(b)
2x^2=6kx-9
k=(11/6)x
2x^2=6[(11/6)x]x-9
2x^2=(11x^2)-9
9x^2=9
x^2=1
x=+1, -1
P點的座標(x, y)=(+1, 2), (-1, 2)
(y=2x^2)[y=2(+1)^2][y=2(-1)^2]