Question

what is C so that y=2x+3 is tangent to the curve y+x^2 +C?

Answer 1

i think that's y=x^2 +C, right ?

Answer 2

if yes, first
take y1=y2, we get a quadratic equation
and then to find value of c, take D=0 (D=discriminant)
solve for c?

Answer 3

yes, thats what I was thinking, do they mean y=x^2 +C

Answer 4

did u get it?

Answer 5

y=2x+3...........i
y=x^2+C........ii

Answer 6

Now, substitute eqn i in eqn ii and tell me what u get

Answer 7

If you want to see the calculation look at the attached file.

Answer 8

thank you very much guys for the help! can I ask why is the D=0 (D=discriminant)?

Answer 9

descriminant is 0 because it is a tangent to the curve, when the descriminant is 0 it has a repeated root, so it just touches the curve, if it were to be greater than 0 it would have two roots which means it would no longer be a tangent, if it were less than 0 it would have two complex roots, not being a tangent,