Given the curve with parametric equations, find the slope and the equation of the tangent line at the indicated x = Vt x = t² y = = (t2 – 4) , t> 0, at the point (2,3) y = t3 – 3t , at the point (3,0) and and

Q: Consider the parametric curve defined by x = t – 7, y = t* + 13t. What is %3D - the slope of the…

A:

Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…

A: The equation of tangent line to the curve is given below

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = 2t3 -…

A: Topic- application of derivatives and tangent equation

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A:

Q: Find parametric equations for the tangent line of the curve r(t) = (3+ 3/7, to – 5t2 + 4, 3t³ + 2t²…

A: Find the parametric equations fot the tangent line

Q: Find the points on the parametric curve c(t) = (3t2 − 2t, t3 − 6t) where the tangent line has slope…

A: Given curve: So,

Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

A:

Q: find the parametric equations for the tangent line to the curve x=t^2-1,y=t^3+1,z=t^2 at the point…

A: Given, x=t^2-1 y=t^3+1 z=t^2 point (x1,y1,z1)= (8,28,9)

Q: The graph of the curve described by the parametric equations x = 2t2 and y =t³ – 3t has a point…

A:

Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

A:

Q: x = 2t2 – C : 3t + 1 y = et²-1

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: given parametric equations are x=1+12t , y=t3-t , z=t3+t

Q: Find the points on the parametric curve c(t) = (3t^2 -3t, t^3 -6t) where the tangent line has slope…

A:

Q: Find the equation for the line tangent to the parametric curve: t3 – 25t 25t2 – 14 at the points…

A:

Q: Find the length of the curve defined by the parametric equations 3 -t, y = 3 In((t/4)? – 1) x = 4…

A: Given:- x =(3t/4)  y = 3ln((t/4)2-1)  To find:- Length of curve from t =5 to t=6

Q: find the slope of the parametric curve x=-6t-5, y=3t^3, at the point t=3

A: To find the slope we have to find dy/dx For that we find dx/dt and dy/dt first

Q: Find the second derivative in terms of t for the parametric equations below- x=t² -t+2 y =t -3t

A: Given that, the parametric equations are x=t2-t+2 and y=t3-3t Find the first derivative in terms of…

Q: Find the slope of the tangent to the parametric curve c(t) = (cos t, sin t) at the point (-1/2,-V3).

A:

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

A:

Q: The derivative I of the parametric equations and y=5vt is

A:

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = sin2(t), y =…

A: Given parametric equation is

Q: find the equations of the tangent and normal to the curve expressed in parametric form at the point…

A:

Q: Find the points on the parametric curve c(t) = (3t 2 − 2t,t 3 − 6t)where the tangent line has slope…

A: This question is taken from the tangent and normal in which we have to find points on the given…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: A curve C is defined by the parametric equations x(t) y(t) = 8t³ – 2t² + 4. Write the equation of…

A:

Q: Find an equation of the tangent(s) to the curve with parametric equations x = t cost, y = tsin t…

A: Given- x=tcost , y=tsint To find - To find the equation of tangent to the curve with given…

Q: Find the parametric equations for the line through the point (0, 1, 2) that is perpendicular to the…

A:

Q: Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the…

A:

Q: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

A:

Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = t3 +…

A:

Q: Find parametric equations for the tangent line at t=3 for the motion of a particle given by…

A: To work out the equation of the tangent in terms of t

Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

A:

Q: 5. Determine the slope of the tangent line, the the equation of the tangent line, and the concavity…

A: this is the equation of tangent line.

Q: 3. Find the equation of the tangent line to the curve C given by the parametric equations x= e', y=…

A:

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1 + √t, y = e^(t^2)…

A: Given parametric equation of curve x=1+t   y=et2we want to find equation of tangent at  ( 2, e)

Q: Find parametric equations for the tangent line to the curve of intersection of the following two…

A: We have to find parametric equations for the tangent line to the curve of intersection of the given…

Q: Find the equation for the line tangent to the parametric curve: at the points where t = 5 and t =…

A: Solution is given below:

Q: Find the equation of the tangent line to the following parametric equation at the given point. x =…

A:

Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…

A: We find dx/dt and dy/dt from the given equations

Q: Find the equation for the line tangent to the parametric curve: t3 – 9t - 9t2 – t4 at the points…

A:

Q: A parametric curve has the equations x =t+sin t and y= cos t. Calculate and , both evaluated at t=…

A: Use dy/dx= (dy/dt)/(dx/dt)

Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

A:

Q: Find the equation of the tangent line to the curve described by the parametric equation described…

A: To find the equation of the tangent to the curve described by parametric equation x=t4+2y=t3+t3,-2

Q: Find the parametric equations for the tangent line to the curve x=t^4−1, y=t^3+1, z=t^2 at the point…

A: Consider the given curves and points.

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x2 +?…

A: Given      x2 + z2 = 25 and y2 + z2 = 25 at the point (3,-3,4) Let    f(x,y,z) = x2 + z2 - 25  and…

Q: A curve in the plane is defined parametrically by the equations written below. An equation of the…

A:

Q: Consider the smooth parametric curve defined by the equations t (t²-3) { = = 3 (t² - 3)' = where t E…

A: