Questions on conic sections and their properties; the curves formed by the intersection of a plane and a cone. Circles, ellipses, hyperbolas, and parabolas are examples of conic sections.
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proof that intersection of two conic sections will intersect at at least two points.
In the following equation ρ(x,y) returns a constant value for a given coordinate.
n is the normal vector to the surface of the form [P,Q,-1] and s is a direction vector.
Using s = [Sx,Sy,Sz], the ...
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0answers
22 views
Representing conic sections as straight lines
Is there a projection that projects any conic section in a two dimensional orthogonal coordinate system with a focus at the origin into a potentially infinite set of parallel straight lines in a two ...
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1answer
25 views
Determine the Angle of an point in an Ellipse
I would like to know how to determine at which angle a point lies in an ellipse. Suppose I have an ellipse with semimajor and semiminor of 10 and 5 (see ...
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2answers
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What is the rationale for the factor of $4$ in the Conics parabola equation?
The Conics form of a parabola equation is $4p(y-k)=(x-h)^2$ where $(h,k)$ is the vertex of the parabola and $p$ is the distance from the vertex to the focus. (Which is also the same distance from the ...
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2answers
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Computing the Semimajor and Semiminor axis of an Ellipse
I have the equation of the ellipse which is $\frac {x^2}{4r^2}+\frac{y^2}{r^2}=1$ Putting the (4,2) point on the ellipse we get $r^2=8$ so we get the equation $\frac {x^2}{32}+\frac {y^2}8=1$ and the ...
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1answer
49 views
Different curves
I stuck on a following question.
The curve is given by:
$(3-k)x^{2}+(7-k)y^{2}+9x+9y+7=0$ For which parameter $k$ k the curve will present
1)ellipse or circle
2)parabola
3)hyperbola
Thanks a lot!
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2answers
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Finding the Width and Height of Ellipse given an a point and angle
I have ellipse, lets say that the height is half of its width and the ellipse is parallel to x axis. then the lets say the center point is situated in the origin ...
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1answer
40 views
Minimum distance between $x = -y^2$ and $(0,-3)$
Find the minimum distance from the parabola $x + y^2 = 0$ (i.e. $x = -y^2$) to the point $(0,-3)$.
This is a homework question. When I try to use the derivative and substitute $-y^2$ for $x$, I ...
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0answers
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How can I find $\int{\sqrt{\left(b^2-1\right)x^2+1\over-x^2+1}}dx$?
I got this from the perimeter of an ellipse. I came up with the formula: arclength of f(x) for x from a to b=$\int_a^b\sqrt{f'(x)^2+1}dx$. Since an ellipse has the equation: $$\left({x-h\over ...
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1answer
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Incomplete elliptic integral of the second kind and the arc length of an ellipse - does a `simple` relation exist?
Short introduction
For a calculation I am working on I need to determine the arc length $l$ of a part of an ellipse in terms of the major axis $2a$, the minor axis $2b$ and the angle $\phi$.
I ...
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1answer
98 views
How do we know $\pi$ is a constant? [duplicate]
How did the ancient Greeks discover that the ratio of a circle's circumference to its diameter is constant? It does not seem so intuitive. Thanks!
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1answer
36 views
Turning an ellipse into a parabola
Today I was discussing circles, ellipses, hyperbolas, and parabolas in my precalculus class. We did the usual: completing the square, finding the center and radius (radii), etc. etc. But I like to ...
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8answers
2k views
What is the real life use of hyperbola? [closed]
I was doing hyperbola ,I was thinking does it have any real life uses or it just a mathematics theory?
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2answers
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Good books on conic section.
Can anybody suggest me good books for conics section.I want it for IIT-JEE mains and advanced and also for ISC. It should be available in India .
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1answer
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Finding a,b of elipse
Given $x^{2}+y^{2}=R^{2}$, so that we multiply every $x$ by $a$ and every $y$ by $b$, $(a>b)$
And the distance between the focuses of this locus is $48R$, and the area of the rhombus which ...
