All Questions
214
questions
4
votes
1
answer
222
views
Why do derivatives of certain equations relating to circles yield other similar equations? [duplicate]
Possible Duplicate:
Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
We all know that the volume of a sphere is:
$V = \frac{4}{3}\pi r^{3}$
and its ...
- 25.4k
4
votes
1
answer
551
views
Is this a valid proof for the area of a circle?
My teacher challenged my class to prove that the area is
$$A=\pi r^2.$$
We recently learned about Riemann sums, so I thought it would be possible to apply them to them to deriving the formula for the ...
- 186
4
votes
2
answers
302
views
Area of $(x-3)^2+(y+2)^2<25: (x,y) \in L_1 \cap L_2$
Two lines $(L_1,L_2)$ intersects the circle $(x-3)^2+(y+2)^2=25$ at the points $(P,Q)$ and $(R,S)$ respectively. The midpoint of the line segment $PQ$ has $x$-coordinate $-\dfrac{3}{5}$, and the ...
- 1,264
4
votes
1
answer
2k
views
Circular Argument in Proof of Circumference of a Circle using Calculus
I have some doubts in this demonstration:
Prove the Circumference of a Circle is $C=2 \pi r$
The equation of a circle is
$(x-h)^2 + (y-k)^2 = r^2 $
To do computations easier let's consider a circle ...
- 212
4
votes
2
answers
5k
views
Equation of a tangent on a circle given the gradient and equation of the circle
My maths teacher told me this problem was impossible without knowledge of implicit differentiation: is she right?
You are given the equation of the circle $\left(x+2\right)^2+\left(y-2\right)^2=16$ , ...
- 819
3
votes
3
answers
376
views
The wrong way of finding the average distance between two points on a circle
I was trying to find the average distance between two points on a circle and got the following result.
Why is my method wrong?
- 123
3
votes
1
answer
428
views
circles tangent to exponential curve
Circle $C_1$ is tangent to the curves $y=e^x$ and $y=-e^x$ and the line $x=0$, and for $n>1$ circle $C_n$ is tangent to both curves and to $C_{n-1}$, how can I find the radius of any circle $C_k$?
...
- 10.2k
3
votes
2
answers
186
views
Area of a circle which is interior to the parabola
I'm trying to solve the following problem:
Find the area of the circle $x^2+y^2=8$, which is interior to the
parabola $y^2=2x$.
I have my own solution and I want to verify whether it is correct. ...
- 147
3
votes
3
answers
2k
views
Prove that 4 points belong to the same circle by using complex numbers
I have Z1, Z2, Z3, Z4 and they are all complex numbers. I want to prove that they belong on the same circle(C) and its center is O where O = 3
How do I do that? (They actually have equations, I just ...
- 433
3
votes
3
answers
1k
views
Find the radius of the largest circle
In the accompanying diagram, a circle of radius $r$ is tangent to both sides of the right-angled corner. What is the radius of the largest circle that will fit in the same corner between the larger ...
- 61
3
votes
2
answers
175
views
Simplify a formula with 449 terms - Radical circle
Context
The other day I wanted to answer this question.
Which is now closed so doesn't accept answers (but this isn't the important part).
Since I didn't know the topic I went to look it up but I ...
3
votes
3
answers
635
views
Slope of the tangents to the circle $x^2+y^2-2x+4y-20=0$
Find the slope of the tangents to the circle
$x^2+y^2-2x+4y-20=0$.
After I arranged into a standard form, which is $(x-1)^2 +(y+2)^2=25$
Centre point is $(1,-2)$ radius is $5$ unit.
Do I need to do ...
- 53
3
votes
3
answers
151
views
Why does $\vec{F(t)} \cdot \vec{v(t)} = 0$ lead to a circular motion?
Here is a mathematical proof that any force $F(t)$, which affects a body, so that $\vec{F(t)} \cdot \vec{v(t)} = 0$, where $v(t)$ is its velocity cannot change the amount of this velocity.
Further, ...
- 387
3
votes
3
answers
8k
views
If $x^2 + y^2 + Ax + By + C = 0 $. Find the condition on $A, B$ and $C$ such that this represents the equation of a circle.
If $x^2 + y^2 + Ax + By + C = 0 $. Find the condition on $A, B$ and $C$ such that this represents the equation of a circle.
Also find the center and radius of the circle.
Here's my solution, I'm ...
- 383
3
votes
1
answer
2k
views
Define polar coordinates of circle at origin and circle with radius $R$.
Question:
(i) Define in polar coordinates $r = f(\alpha)$ the origin-centred circle with radius $R$. Specify the domain range for the polar coordinate $\alpha$.
(ii) Define in polar coordinates $r = ...
- 35