1. M

    Pre Calculus Help Videos

    Hey guys and girls! I am a current student in college getting a degree in math and have decided to try my best at creating a YouTube channel full of math problems to help students of all ages learn the greatest subject. I am planning on covering PreCalculus first as it can be tough for many...
  2. R

    Conics Parabola

    I took the 124 to the other side then I made the x^2 - 8 a perfect square which adds 16 to 124. I end up with (x-4)^2 - 28y = 140 Then I take 28y to other side. Pull out 28 which leaves 28(y-5). (x-4)^2 = 28(y-5) remains, what am I doing wrong? I think I did it right, 100%
  3. A

    conics ellipse

    hi; Why in ellipses is a^2 - b^2 = c^2. thanks.
  4. K


    Compute the points of the intersection between the circle x^2+y^2=1 and hyperbola xy=1? I tried to put 1/y in place of x but I couldn't solve.
  5. M

    Help solving conics that are equal to zero, degenerate

    If I have a conic in standard form (converted from 9x2 -4y2-36x-24y=0) of 9(x-2)2-4(y+3)2=0, how would I go about either solving or graphing this. If it were a plus sign between them I'd just give an answer of a point, but I have a strange feeling that there is more to the answer, a solution...
  6. froodles01

    Conics: ellipse in standard position

    An example with answer I have goes; x = 6 cos t y = sqrt 11 sin t Write down the equation of the conic & state what type of conic it is. trig identity cos2t + sin2t = 1 which gives x2 / 62 + y2 / (sqrt 11)2 = 1 . . . . . . . . er! how does this happen, if you could help!
  7. L

    Rotation of Ellipse to FIND the Bxy term, from horizontal to an angle of pi/4

    In essence I'm trying to take a horizontal ellipse and put it at an angle, rotating it around the origin. It's for my conics project, I'm making the elliptical orbits of the planets. So I have the a, b, and c terms of the ellipse, (as in the distance from vertice to center and such) which are...
  8. H

    Transformations of conics?

    Write an equation of the translated or rotated graph in general form. y=3x^2-2x+5 T(2,-3) I know the graph is a parabola. But I am not sure where I would "plug in" h and k into this equation. To get the translated equation.
  9. N

    Conics: Hyberbolas

    The question is asking to find the standard form of the equation of the hyperbola with the given characteristics: Verticies: (-2,1), (2,1) Foci: (-3,1), (3,1) using the c^2=A^2 + B^2 I find that a = 2(verticies) and c = 3(foci) so b= √5 Plugging everything back in the standard equation...
  10. N

    Conics: Parabola

    Hello! The question is asking me to find the vertex, focus and directrix of the parabola, and sketch its graph. y= (1/4) (x^2 -2x+5) I tried putting aside the 1/4 for the time being and tried completing the square y-5 = (x^2)-2x y-3 = (x^2)-2x+2 y-3 = (x-1)^2 Plugging back in...
  11. E

    Tangent lines to conics

    I am unable to comprehend the proof for tangent line to conics. Here is the proof as per the book (Multiview Geometry by Hartley and Zisserman). Everything is in homogeneous coordinates. The line l = Cx passes through x, since l(TRANSPOSE) x = x(TRANSPOSE) Cx = 0. If l has one-point...
  12. M

    Oblique Conics?

    Hi, Is it possible to write the equation of an oblique conic in the y= form? For example, the equation 2x^2-4y^2+5xy=1 looks like How do I find the y= version of it? Thanks! -Masoug
  13. A

    Question based on conics

    The following is a 'multiple-option correct' question.. If the straight line 3x+4y=24 intersects the axes at A and B and the straight line 4x+3y=24 at C and D, then the points A,B,C and D lie on: (a) a Circle (b) a Parabola (c) an Ellipse (d) a Hyperbola My attempt: I...
  14. A

    Conics, Rectangular Hyperbola

    Hey guys how do I prove that the angle between the asymptotes of a rectangular hyperbola is 90 degrees I derived the formula from a previous step in the question to find the angle between \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 which was \theta=\tan^{-1} (\frac{2ab}{a^{2}-b^{2}}) so now that...
  15. W

    Conics question

    A straight line D through the focus F of a conic \Phi meets \Phi in two points A and B. Show that the quantity \frac{1}{|AF|} + \frac{1}{|BF|} is independent of the choice of line D. Not sure where to start with this one apart from maybe trying the 3 different conics of hyperbola, parabola and...
  16. X


    Hi For the parabola y = 0.5 (x^2 +1), why is the equation of the tangent at point P (a,b): xa = y + b -1 (in the textbook)? I tried differentiating the parabola equation to find the gradient (a) and then using y-y1 = m(x-x1) formula but it doesnt turn out to be that... Please help?!?
  17. L

    Conics - Distance between Two Points on Circle

    R (x, y) P (a,b) Q (c,d) are points on x^2 + y^2 + 2gx + 2fy +k = 0 i) if d is the distance between points R and P, show that: -d^2/2 = x.a + y.b + g(x+a) + f(y+b) + k I am not sure how to begin this question. Any approach is possible. Thanks guys
  18. G


    Im stuck in the part in red, I need help. I've done the rest already. Some of my answers: maybe this thread also belongs in this subforum:
  19. H

    Graphing Conics

    4x^2 + 4y^2 +20x -16y + 37 =0 I completed the square and got: (2x+10)^2 + (2y-8)^2 =127 x int ? y int ? Vertices ? Center (-5, 4) Domain ? Range ? I tried making y=0 to find the x intercepts but didn't work out. Same thing for y intercepts Completely lost....
  20. A


    Hello! I have like 3 problems: a. Produce a conic system of inequalities representing the "doughnut-shape" created by an ellipse inside a circle. b. Produce a conic system that has exactly two points of intersection and consists of a circle and ellipse with the same area. c. True or...