Question

The curve y=x^2+ax+b and y=cx-x^2 have common tangent line at (1,0) find a ,b, c?

Answer 1

i have try to solve but at end i am confused please solve it.
i have find tangents of both curves and equate them,then find the equation of tangent which must be equall but its not coming equal diffrence in x^2 value sign

Answer 2

dont equate the equation of tangents..
if two equations are identical then ratio of coefficients are equal

Answer 3

suppose a1x+b1y+c1=0 and a2x+b2y+c2=0 are identical equations then a1/a2=b1/b2=c1/c2

Answer 4

i assume it means both curves pass through (1,0) and also just touch each other at that point

so you'll have
1+a+b = 0
and
c-1 = 0

tangent at x=1 for second eqn = c- 2
and for 1st one is 2+a
=> c-2 = 2+a

you may now easily solve for a,b,c..

i may have mistreated the question though,please correct me of am wrong somewhere..