Question

Find the equation of all lines having slope 2 which are tangents to the curve .

Answer 1

The equation of the given curve is,

y= 1 x−3 , x≠3

The slope of the tangent at any point ( x,y ) is given as,

Slope= dy dx

The slope of the given curve is,

dy dx = d( 1 x−3 ) dx = −1 ( x−3 ) 2

When the slope of the tangent is 2, then

−1 ( x−3 ) 2 =2 2 ( x−3 ) 2 =−1 ( x−3 ) 2 = −1 2

The above condition can never be satisfied for any value of x, so there is no tangent with slope 2 to the given curve.