Class 12

Math

Calculus

Application of Derivatives

Find the equation of all lines having slope 2 and being tangent to the curve $y+x−32 =0$.

$y+x−32 =0$

Differentiating it w.r.t. $x$,

$⇒dxdy −(x−3)_{2}2 =0$

$⇒dxdy =(x−3)_{2}2 $

Now, it is given that slope of the tangent is $2$.

$∴dxdy =2$

$⇒(x−3)_{2}2 =2$

$⇒(x−3)_{2}=1$

$⇒x−3=±1$

$⇒x=4andx=2$

When $x=4$,

$y+4−32 =0$

$⇒y=−2$

So, equation of tangent with this point,$y+2=2(x−4)⇒2x−y=10$

When $x=2$,

$y+2−32 =0$

$⇒y=2$

So, equation of tangent with this point,$y−2=2(x−2)⇒2x−y=2.$