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hyperbola

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A rectangular hyperbola 2013-09-19
From Soumya:
Is the graph of an inverse variation a RECTANGULAR HYPERBOLA? If it is, then how can be the equation of a rectangular hyperbola be xy=constant , whereas in the books it is written that the graph of a rectangular hyperbola is- x^2-y^2=a^2?
Answered by Chris Fisher.
A rectangular hyperbola 2007-11-06
From Gareth:
2. Consider the rectangular hyperbola xy = c2 with parametrization (x, y) = (ct, c/t), and t 6= 0.
i. Derive (i.e. do not just quote) the equations of the tangent and normal at the point P with (parametric) coordinates (cp, c/p).
ii. Consider the points P : (cp, c/p) and Q : (cq, c/q) on the hyperbola. Find the equation of the straight line that joins the points P and Q.
iii. Consider a point R : (cr, c/r) also on the hyperbola, and suppose that in the triangle PRQ, \PRQ = 90◦. Prove that the normal (to the hyperbola) at R is parallel to the line PQ.

Answered by Harley Weston.
Sketch the graph of the hyperbola and its asymptotes 2007-03-13
From Katrina:
Given (y-2) ^2 x^2/4 =1 do the following: Sketch the graph of the hyperbola and its asymptotes. Label the vertices on the graph I attached the graph thanks for your help!
Answered by Penny Nom.
Conic sections 2006-11-19
From Joyce:
My son has a project on conic sections. I need the following information on Parabola, Circle, ellipse,and hyperbola. He can't find the following information for each conic section: equations with explanations, four uses for each shape and Shape explanation.
Answered by Penny Nom.
Some applications of conic sections 2006-11-13
From Burt:
how are circles, ellipses, and hyperbolas used in everyday life
Answered by Penny Nom.
Find the xy equation of the curve on which Brian is located. 2006-02-20
From Skye:
Andrew, located at (0, -2200) fired a rifle. The sound echoed off a cliff at (0,2200) to Brian, located at point (x,y). Brian heard the echo 6 seconds after he heard the original shot. Find the xy equation of the curve on which Brian is located. Assume the distances are in feet and that sound travels at 1100 feet/second. (hint: find the equation of the hyperbola)
Answered by Stephen La Rocque.
A conic 2004-08-10
From A student:
My question is about this equation 32x*2 -18y*2 -64x +72y +248 =0 explain why as x goes to the infinity the graph of the conic looks like y= (3/4)X.

What I did to try to find the solution of this problem was to graph and then I thought that maybe trying to find the equation of the asymptotes I could do it, but it was useless -because the equation of the asymptotes is y= +4/3(X-1) -2 and that does not explain why tho conic looks like y=(3/4) x . I would really appreciate your help on this.

Answered by Penny Nom.
A tangent to a hyperbola 2004-08-02
From A student:
The equation of a hyperbola is 32x*2 -18Y*2-64x +72y +248=0. The equation of a tangent line to this hyperbola is y= (16/15)X + 10/3 I have been trying to find the point where this line intersects the graph. What I did was solve for x and then plugged in the result into the equation of the hyperbola, but I am getting two answers and I am supposed to get only one because the line is tangent to the graph. For this reason, I would like to know what I am doing wrong or what I have to do to know which answer is correct.
Answered by Penny Nom.
Uses of conic sections 2003-04-01
From William:
My name is William and I am doing a research paper on conic sections for my 12th grade math class. Part of the project is to find two conic sections in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where conic sections are used in our world today and I really can't find anything. If you can tell me specific building or a pyramid that contains conic sections that would be great. Or even something in the universe would be helpful.
Answered by Leeanne Boehm.
A cone in 3 space 2002-03-20
From Matthew:
Let C in R3 be the cone defined by x2 + y2 - z2 = 0

(A) Let P be the plane described by x + 2z = 1

(i) Find a description of P in terms of two parameters s and t

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Answered by Walter Whiteley.
A hyperbola centered at (0,0) 2001-12-28
From Carla:
  1. Find the equation of the hyperbola centered at (0,0) with vertices at (0,3) and (0,-3) that is asymptotic to the lines y=+-5x.

  2. Find the equation of a hyperbola in standard position foci (1,5) and (1,7) and eccentricity 2.

Answered by Peny Nom.
Circles, ellipses, parabolas and hyperbolas 2001-05-09
From Colleen:
How is an ellipse like a circle?
In what way does an ellipse have a center?
How is a hyperbola similar and different to an ellipse?
How is a parabola similar a different to a circle ellipse and parabola?

Answered by Pnny Nom.
Rectangular hyperbola 1999-12-15
From Aarti Chand:
Why do they call a rectangular hyperbola, rectangular and where the normal hyperbola looks like a rectangle and the rectangular hyperbola looks like a sqaure?
Answered by Chris Fisher.
 
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