For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 5?

Answer 1

the slope of 2x+y = b is -2

the slope of y = ax^2 is
dy/dx = 2ax
so when x = 5
2a(5) = -2
a = -2/10 = -1/5

so the parabola is y = (-1/5)x^2
when x=5, y = -5

but that point (5,-5) must also be on the tangent
2(5)+5 = b
b = 15

so a= -1/5 and b=15

Answer 2

for B the answer would be 5, the point (5,-5) when plugged into the the 2x+y=b equation gives you 2(5)+(-5)= b
b=5