Find the equation of the line tangent to the graph of x(t)=t²+1 and y(t)= at point t=3​

The equation of the straight line

  x - 24y + 38 =0

Step-by-step explanation:

Step(i):-

Given that x(t) = t²+1 ..(i)

        and y(t) = √1+t  ..(ii)

Differentiating equation(i) with respective to 't'

Differentiating equation(ii) with respective to 't'

Step(ii):-

The slope of the tangent

Step(iii):-

Point   x = t²+1 = 3²+1 = 10

          y = √1+t =√1+3 = √4 =2

The point on the tangent line is ( 10 ,2)

The equation of the straight line

   24 (y-2) = x-10

   24y - 48 = x-10

    x - 24 y -10 +48 =0

   x - 24y + 38 =0

Final -

The equation of the straight line

  x - 24y + 38 =0

it is probably the graph on the bottom right.