Thread: tangent with "unknown parabola"

im sorry for posting so many questions. this is the last.

"the line is a tangent to the parabola at the point (1,2). find a and b"

now i have no idea where to start here. i could assume solving simultaneuosly could give some sort of answer but it would contain both unknowns.

if i differentiate i get

and from the tangent we know that
at (1,2)

its here that im confused. whether the whole previous section is wrong i just cant get an answer.

Originally Posted by link0099

im sorry for posting so many questions. this is the last.

"the line is a tangent to the parabola at the point (1,2). find a and b"

now i have no idea where to start here. i could assume solving simultaneuosly could give some sort of answer but it would contain both unknowns.

if i differentiate i get

and from the tangent we know that
at (1,2)

its here that im confused. whether the whole previous section is wrong i just cant get an answer.

Just consider again what you are given, and use what you already have.
First, because the parabola must pass through the point (1,2) you must have that

Second, since the given line with slope 5 is to be tangent to the parabola at point (1,2) you must also have that

In other words, you have a system of two linear equations for a and b. - Solve it. - Done!

so simultaneously solved we get (2) - (1)

and sub a=3 into (1)



is that right

therefore parabola eqn =


maybe?

Originally Posted by link0099

so simultaneously solved we get (2) - (1)

No, I think you get a=2

and sub a=3 into (1)



is that right

Not quite, you get b=1

therefore parabola eqn =

maybe?

would be more likely correct, I think.

oh yes 2 makes more sense. thanks a lot

Check the calcualtions.

a+b = 3...(1)

2a + b = 5 ...(2)

Now solve for a and b.