Solve problems relating to parametric curves

Plot a curve for parametric equation and for

In which two quadrants is the curve present for the given range of t?

Sketch the following curve by plotting points for the parameter "t" when : where

Also which of the following is the correct description of the type of curve?

Write parametric equation for Ellipse with center at (2,3), width along x-axis as 3 and y-axis as 10. Also plot the curve for interval 0<t<6.5

Which is correct option for the equation of ellipse?

Plot the 2-D curve for parametric equation x = 5 sin(t) and y = 3 cos(3t) for 0<t<10

How many times does the curve intersect itself?

Write the parametric equation for the path traced by a point on bicycle wheel. (A cycloid) If the wheel is 1.4m in diameter, plot the path traced by it for 6 secs. What is the equation for this cycloid?

Plot the 2-D curve  for

In which quadrants would the sketched curve be present?

Plot the logarithmic spiral expressed by following parametric equations for interval of -15 < t < 15. 

What is the nature of curve?

1. Match the following parametric equations in column A with their implicit equation in column B

Column A: Parametric Equation		Column B: Implicit Equation
1		a
2		b
3	x=t	c
4	x=a cos (t)+h y=b sin (t) +k	d	mx-y=b
5	x=a sec (t)+h y=b tan (t)+k	e
	x=a tan (t)+h y=b sec (t)+k	f

1. Match the following parametric equations in column A with their representative plot in column B

Find the slope of line presented with parametric equations (3+t, t)

Write the parametric equation of circle with radius as 4m and center as (-1,3) and find the slope of tangent at t = 5.

If the parametric curve is defined by and , find the slope of tangent at t = 0.

Find the equation of tangent for the conjugate hyperbola with center at origin, a = 2 and b = 3 at t = 3

Plot the 2-D curve with parametric equations as below for -10 < t < 10

,       

Find the equation of tangent at t = 0 and comment on its characteristics and list of points that will share same tangent.

1. Find the equation of tangent to the 2-D curve represented equations below at t = 6. Plot the curve for interval 0 < t < 8 and tangent. 

x=sin (t) +t

y=cos (2t)