Curves defined by parameteric equations

Consider the following.
x = e^t - 12
y = e^2t
(a) Eliminate the parameter to find a Cartesian equation of the curve.

  1. 👍
  2. 👎
  3. 👁
  1. from x = e^t - 12
    e^t = x+12
    t = ln(x+12)

    form y = e^2t
    2t = lny
    t = (lny)/2

    so (ln y)/2 = ln(x+12)
    lny = 2ln(x+12)
    lny = ln(x+12)^2
    y = (x+12)^2

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-Calc

    Eliminate the parameter x = t^2 - 1 and y = t^2 + t

  2. Chemistry

    Which one of the following compounds does not follow the octet rule? a) NF3 b) CF4 c) SF4 d) PH3 e) HCl I know I can eliminate A and B because nitrogen and carbon follow the octet rule. I know I can eliminate E because the total

  3. Algebra/Precalculus

    Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x, y, and z in terms of the parameter a.) 3x-3y+6z=6 x+2y-z=8 5x-8y+13z=4

  4. Probability

    Confidence interval interpretation Every day, I try to estimate an unknown parameter using a fresh data set. I look at the data and then I use some formulas to calculate a 70% confidence interval, [Θˆ−,Θˆ+], based on the


    Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations. x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π A. x2 - y2 = 6; -6 ≤ x ≤ 6 B. x2 - y2 = 36; -6 ≤ x ≤ 6 C. x2 + y2 =

  2. math-precalculus

    Eliminate the parameter t to find a Cartesian equation in the form x=f(y) x(t)=4t^2 y(t)=4+2t

  3. Calculus

    Eliminate the parameter for the following parametric equations: x(t)=t-2 y(t)=t^2-4 A) y=x^2+2x+8 B) y=x^2+4x+4 C) y=x^2+4x D) y=x^2+4x+8

  4. calculus

    Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=4+2cos(theta) y=-1+2sin(theta)

  1. geometry

    The angle of depression from the top of a lighthouse to a boat in the water is 30°. If the lighthouse is 89 feet tall how far is the boat from the lighthouse to the nearest foot? Answers available in ... 10Take this time to do

  2. English

    1) The tea was cold, the fire was dead; What figurative language is this? A)assonance Eliminate B)onomatopoeia C)alliteration D)internal rhyme 2) Which stylistic or literary device is used in the line: ‘Sick with a fear that had

  3. Calculus

    Eliminate the parameter for the following set of parametric equations X(t)=t^3 Y(t)=t-6 A) y=(x-6)^3 B) y=^2sqrtx-6 C) y=t^3-6 D) y=x^3-6

  4. Calc

    A curve is given by parametric equations x=t^2−1,y=t+1. Eliminate the parameter t to find a Cartesian equation of the curveSimplify your answer

You can view more similar questions or ask a new question.