maths - geometry -yr11

HI guys.

find the equations of the lines represented by

4x^2 - 5xy - 6y^2 + 11x + 11y - 3 = 0

I am lost. What two lines are they asking for? And is there a general formula/appraoch to simplifying the duel equation with powers to 2?
I tried turning the x^2 and y^2 into squares but then I was left with the 5xy not knowing what to do. Please help.

  1. 👍
  2. 👎
  3. 👁
  1. It is a conic. First use the discriminant theorem to figure out what conic it is
    A x^2 + B x y + C y^2 + D x + E y + F = 0
    B^2 -4 A C
    negative - ellipse
    0 - parabola
    positive - hyperbola
    here B^2 - 4 A C = 25 - 4*4*(-6)
    = 25 + 96 = +121 so it is a hyperbola
    the axis of the hyperbola is at an angle to the x axis though, resulting in the xy term with coefficient -5
    They may be asking for the directions of x' and y' that make this a decoupled hyperbola with no xy term. I do not know.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Which graph best represents the solution to the following pair of equations? (1 point) y = −x − 5 y = 2x + 4 A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines

  2. can you answer this very quick

    On a graph, the solution to a system of linear equations will be represented by ______. A. the x-intercept of each line B. the y-intercept of each line C. all the points on either line D. the intersection of the lines

  3. math

    What will the graph look like for a system of equations that has no solutions? A. The lines will be perpendicular. B. The lines cross at one point. C. Both equations will form the same line. D. The lines will be parallel. Is the

  4. calculus

    Find equations for the lines that are tangent and normal to the graph of y = sinx + 3 at x = pi

  1. math

    Consider the following system of equations. {y = 3x − 5 {y = −x + 7 a. Are the graphs of the two lines intersecting lines, the same line, or parallel lines? Explain your reasoning. b. How many solutions does the system have?

  2. Geometry

    Examine the two distinct lines defined by the following two equations in slope-intercept form. line ℓ: y=34x+6 line k: y=34x−7 Are lines ℓ and k parallel? Justify your response. 1.Yes, lines ℓ and k are parallel because


    3. What is the rule for the function shown in the table? (1 point) x = -1, 0, 1, 2 y = -2, 1, 4, 7 A.y = 1/3x + 1 B.y = 3x + 1 C.y = 1/3x D.y = 1/2x + 1 4. What is the function rule for the following situation? rex paid $20 for a

  4. math

    Find the slope of the lines that are (a) parallel lines (b) perpendicular lines to the lines passing through the pair of points (3, 4)(2,-1)

  1. writing thesis

    So, I need a thesis statement for a research paper for Murder on the Orient Express. (Sorry to keep posting a new question each time) But I've thought about the answers you guys have given me and I'm thinking something along the

  2. maths

    P(6,3), Q(3,7), and R(4,2) are three points in a plane. A is the midpoint of QR and B is the foot of the perpendicular from Q to PR. Find;- (A) the cordinates of A; (B) the equations of the lines PA and QB; (C) the point of

  3. Math

    1. Two lines, C and D, are represented by the following equations: Line C: y = x + 5 Line D: y = −2x − 1 Which of the following options shows the solution to the system of equations and explains why? (−2, 3), because the

  4. algebra

    Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x - 4y = -3 8x + 6y = -3

You can view more similar questions or ask a new question.