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)