Question

Find the equation of the tangent to the curve which is parallel to the line 4 x − 2 y + 5 = 0.

Answer 1

The given equation of curve is,

y= 3x−2

The equation of slope of the tangent to the curve is,

dy dx = 3 2 3x−2

The equation of the given line is,

4x−2y+5=0 y=2x+ 5 2

Compare the above equation with y=mx+c.

m=2

Here, m is the slope of the line.

It is given that the line is parallel to the slope of the tangent, then,

3 2 3x−2 =2 3x−2 = 3 4 3x−2= 9 16 x= 41 28

The coordinate of y when x= 41 28 is,

y= 3( 41 28 )−2 = 3 4

Equation of tangent from a point ( x 1 , y 1 ) is given as,

y− y 1 =m( x− x 1 )

Equation of tangent from a point ( 41 48 , 3 4 ) is given as,

y− 3 4 =2( x− 41 48 ) 48x−24y=23

Therefore, the equation of the tangent is 48x−24y=23.