Question
The radius of curvature for the parabola $x=a, y=2 a t$ at any point $t=\ldots \ldots \ldots .$
Step 1
Given the parametric equations of the parabola, x = a and y = 2at, we can express y in terms of x as follows: y = 2at = 2a(x/a) = 2x So, the equation of the parabola is y = 2x. Show more…
Show all steps
Your feedback will help us improve your experience
Malika Singh and 60 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The radius of curvature at any point $\mathfrak{t}^{\prime}$ on the curve $\mathrm{x}=2 \mathrm{t}, \mathrm{y}=\mathrm{t}^{2}-1$ is (a) $\frac{\left(1+\mathrm{t}^{2}\right)^{3 / 2}}{2 \mathrm{t}}$ (b) $\frac{\left(1+\mathrm{t}^{2}\right)^{3 / 2}}{2}$ (c) $\left(1+t^{2}\right)^{3 / 2}$ (d) $2\left(1+t^{2}\right)^{3 / 2}$
Find the radius of curvature of the parabola $y^{2}=4 p x$ at $(0,0) .$
VECTOR-VALUED FUNCTIONS
Curvature
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD