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
    where
    A x^2 + B x y + C y^2 + D x + E y + F = 0
    if
    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. 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

  3. 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

  4. Geometry

    Find the distance between the lines with the equations y = 3/2x+4 and −3x+2y = −1. Round your answer to the nearest tenth.

  1. 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)

  2. cal

    Equations of the tangent lines to hyperbola xy=1 that pass through point (-1,1) I know the graph of y=1/x but not sure about the tangent lines at given point. Are the lines tangent to (1,1) and (-1,-1)? You're correct, the graph

  3. MATH PLS HELP CHECK ANSWERS

    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

    Consider the following systems of equations: y= .5x-1 y= .5x+4 Are the graphs of the two lines intersecting lines, the same line, or parallel lines? How many solutions does the system have? A) No solution: The lines are parallel

  1. algebra

    Given an equation of a line, find equations for lines parallel or perpendicular to it going through specified points. Find the appropriate equations and points from the table below. Simplify your equations into slope-intercept

  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

    Find the equations of at least three lines that intersect each other at the point (6, -2).

  4. Art

    By asking questions such as, "Look at the lines on your paper and on the ceiling. Can you find other lines? Thin lines? Thick lines? " a teacher is building children's conception of a. depth perception b. creativity c. perspective

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