If the tangent to the curve y=x3-x2+x at the point (a , b) is also tangent to the curve y=5 x2+2 x-25 at the point (2,-1), then |2 a+9 b| is equal to

Question

If the tangent to the curve y=x3-x2+x at the point (a , b) is also tangent to the curve y=5 x2+2 x-25 at the point (2,-1), then |2 a+9 b| is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

y=5 x2+2 x-25 P(2,-1) y prime=10 x+2 yP prime=22 ∴ text tangent to curve at P y+1=22(x-2) y=22 x-45

.( dy / dx )| C 2=3 x 2-2 x +1 .( dy / dx )| Q =3 a 2-2 a +1 Hence 3 a2-2 a+1=22 ∴ 3 a2-2 a-21=0 3 a2-9 a+7 a-21=0

a=3 b=21 |2 a+9 b|=195 at a =-7 / 3 tangent will be parallel Hence it is rejected

Q. If the tangent to the curve y=x3−x2+x at the point (a , b) is also tangent to the curve y=5x2+2x−25 at the point (2,−1), then ∣2a+9b∣ is equal to

Q. If the tangent to the curve $y = x^{3} - x^{2} + x$ at the point (a , b) is also tangent to the curve $y = 5 x^{2} + 2 x - 25$ at the point $(2, - 1)$ , then $∣2 a + 9 b ∣$ is equal to