AP EAPCET 04-Jul-2022 Shift 1 Paper

‌y=x3−3x2−8x−4
‌y=3x2+7x+4
∵ Curves touch each other.
‌∴‌‌x3−3x2−8x−4=3x2+7x+4
‌⇒‌‌x3−6x2−15x−8=0
On putting x=−1
‌ LHS ‌‌=−1−6+15−8
‌=−15+15=0= RHS
On putting x=−1 in any curve equation,
y=−1−3+8−4=0
∴(−1,0) is the intersection point.
Equation of tangent,
y−y1=m(x−x1) .......(i)
y‌=x3−3x2−8x−4
y′‌=3x2−6x−8
y′|(1−1,0)‌=3+6−8=1⇒m=1
Put the values into Eq. (i),
‌y−0=1(x+1)
⇒y=x+1
⇒x−y+1=0