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Questions tagged [parametric]

For questions about parametric equations, their application, equivalence to other equation types and definition.

In mathematics, a parametric equation of a curve is a representation of this curve through equations expressing the coordinates of the points of the curve as functions of a variable called a parameter. This contrasts with implicit equations that define a curve as the zero set of some equation in the coordinates.

The parametric forms of curves are well-suited for drawing on a computer, while their corresponding implicit forms are useful for analytic manipulations (intersections, etc.)

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Parabola Question - simultaneous equations?

I'm having trouble with the second part of this question. I can do the first part by finding the normal at P and where it intercepts with U and then for the second part i've substituted each point into the first equation...I don't know where to go…
Bob
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Use the discriminant to show that $mx−y + m^2 = 0$ touches the parabola $x^2 =−4y$, for all values of m.

Use the discriminant to show that $mx−y + m^2 = 0$ touches the parabola $x^2 =−4y$, for all values of m. I attempted to solve by letting them both equal each other, but it didn't work. How do I do this question? Thank You in advance.
006609
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Find, in terms of $s$,the coordinates of the point where this normal cuts the curve again.

a) Find the equation of the normal at the point $(2s,\frac{2}{s})$ to the curve whose parametric equations are $x=2s,y=\frac{2}{s}$ b) Find, in terms of $s$,the coordinates of the point where this normal cuts the curve again. I didn't have any…
Rogerc1979
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How a formula is developed

The rule for converting line equations to parametric equations is: $$\frac{(x-x_1)}{a} =\frac{(y-y_1)}{b} =t$$ I would like to know how this was developed. Thank you.
JOhn John
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Slope of a Parametrized Curve

Say that we have the parametrized curve $x=e^{3t}, y=te^{-t}$. What would be the slope of this at the point $(1,0)$ and also on which points on the curve would the curve be horizontal? What I have done: For the first question, I used…
Isaac
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What Parametric Equations are required to move along a circle while moving left?

I'm working on a program where I can set objects along arbitrary parametric paths. Moving left is easy: X = x - dT(V) Y = y Moving in a circle is easy: X = x+ Cos(dt*Pi) Y = y+ Sin(dt*Pi) So I tried to combine them to move left while also moving in…
Raven Dreamer
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Parametric equation question showing minimum value of d^2

for the equation $d^2 = (1-a)^2t^2 + 18(1-a)t +117$ Show that when $a = 2$, the minimum value of $d^2$ is attained when $t=9$. I set $a=2$ to get $d^2 = t^2 - 18t + 117$ should i now just run it with $t = 9$ ? this gets an answer of $d^2 = 36$ $d=6$…
Mathsguy9020
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How to parameterize a straight line?

Why does the straight line from $(x_1,+y_1,+z_1)$ to $(x_2,+y_2,+z_2)$ become $r(\vec t)=(1-t)(x_1,+y_1,+z_1)+t(x_2,+y_2,+z_2)$ for $0 \leq t \leq 1$?
Ryan
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Consider the parametric curve given by: $x=3\cos(t)$, $y=t^{3/2}$.

The question asks to find the equation of the tangent to this curve at the point $t=\pi/4$. I've determined $$\frac{dy}{dx} =(\frac{dy}{dt})/(\frac{dx}{dt}) = -0.222$$ Have I got the right idea? Also asks for the solution to be in the form $y=mx+c$,…
AidanLeith
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Eliminating the parameter?

How would you eliminate the parameter where the x coordinate is in terms of t, but the t is squared. x= 3t - $t^2$ y= t + 1 I know to solve for y as a function of x, but I'm not sure how to do so with powers.
Steven T
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Parametrisize of vertecies (0,0) (a,0) (0,b)

Hi i have been given 3 vertecies. (0,0) (a,0) (0,b) The constants a and b are >=0. This forms a backwards triangle. The parametisation don't make sense to me, so basically what i am asking is for someone to explain it to me in a way that makes sense…
Corvo
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A curve is described in polar coordinates . Find parametric equations for $x$ and $y$ and plot the curve.

A curve is described in polar coordinates by the equations $$ r = t; \theta = 3 \cos t; 0 ≤ t ≤ 10 $$ Find parametric equations for $x$ and $y.$ I cannot convert it into parametric form
user221733
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Intersection of two parametric equations

This is a super basic question I'm sure but I can't figure it out and that's so frustrating. I must, in this homework problem (yes it is homework, so please do not give away the answer but rather make suggestions or give hints), find the…
bjd2385
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figuring out parametric equation of a moving dot of specific velocity along acurve

I currently need to model a dot moving along an arbitrary curve given it's velocity, initial point, and $y=f(x)$ form of equation. I vaguely remember from my high school teaching that it will possibly require using differentiation, integration, and…
inyeol
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Finding the points of intersection between parametric equations and a circle.

A curve has the equation $ x=2t^{2} $ and $ y=3t $ and a circle has the equation $ x^{2} + y^{2}-6x-1 =0 $ What are the coordinates of the intersections between the objects? I tried subbing the x and y equations into the circle formula. This…
Tomato721
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