AP EAPCET 23-Aug-2021 Shift 2 Paper

Given curve, y=x2−3x+2
On differentiating w.r.t. x ,

dy

dx

=2x−3
Which represents the slope of tangent drawn to the curve.
m1=2x−3 ...(i)
Given line, y=x ...(ii)
On comparing with y=mx+c
Slope of line (ii), m2=1
∴ Tangent to the curve is perpendicular to line (ii).
∴m1.m2=−1
⇒m1.1=−1
⇒m1=−1
⇒2x−3=−1
⇒2x=2
⇒x=1
⇒y=(1)2−3×1+2
⇒y=0
∴ Point of tangent drawn =(1,0)