For each real number a, the line y = (2a + 3) x - a^2 intersects the curve y = x^2 + 3x at precisely one point. Find the line intersecting the curve at the point (2/3, 22/9).
+128408 We only need to solve this
22/9 = (2a + 3)(2/3) - a^2
22/9 = (4/3)a + 2 - a^2 rearrange as
a^2 - (4/3)a + 22/9 - 2 = 0
a^2 - (4/3)a + 4/9 = 0 factor as
(a - 2/3)^2 = 0
a = 2/3
The line is
y = (13/3)x - 4/9
See the graph here : https://www.desmos.com/calculator/oxhhombjut
