posted by .

A curve has implicit equation x^2-2xy+4y^2=12

a)find the expression for dy/dx in terms of y and x. hence determine the coordinates of the point where the tangents to the curve are parallel to the x-axis.

b)Find the equation of the normal to the curve at the point (2sqrt3,sqrt3).

  • math -


    2x - 2x dy/dx - 2y + 8y^ dy/dx = 0
    dy/dx(8y^2 - 2x) = 2y - 2x
    dy/dx = (y-x)/(4y^2-x)

    to be horizontal to the x-axis, the slope must be zero, that is, dy/dx = 0
    so y-x = 0
    y = x

    plug that back into the original
    x^2 - 2x^2 + 4x^2 = 12
    3x^2 = 12
    x = ±2

    two points: (2,2) and (-2,-2)

    b) plug the x and y values into dy/dx to get the slope
    take the negative reciprocal to get the slope of the normal
    use your grade 9 method to find the equation, now that you have the slope m and a given point.

    (I had y = -2x + 5√3 )

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point?
  2. Calculus - Maths

    I got a few questions. Hope ya'll can help out. 1) for F(X) = 6x - 2x^2 Find the gradient of the chord joining the point where the X coorinates are 1 and (1+h) respectively. b) hence find the gradient at x=1 2) Find the Coordinates …
  3. calculus

    there are two tangents lines to the curve f(x) = 3x^2 that pass through the point p =0,1 find the x coordinates of the point where the tangents line intersect the curve
  4. 12th Grade Calculus

    1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5) [* for a. the answer that I obtained was y-5 = -1/18 (x-3) ] b.) What is the smallest slope on the curve?
  5. calculus

    1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve …
  6. calculus

    Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve …
  7. calculus

    A curve passes through the point (1,-11) and it's gradient at any point is ax^2 + b, where a and b are constants. The tangent to the curve at the point (2,-16) is parallel to the x-axis. Find i) the values of a and b ii) the equation …
  8. Ap calc.. Dying!! Please help!

    Given the curve x^2-xy+y^2=9 A) write a general expression for the slope of the curve. B) find the coordinates of the points on the curve where the tangents are vertical C) at the point (0,3) find the rate of change in the slope of …
  9. Calculus

    A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show your …
  10. Math Calculus (ALEVEL)

    Find the equation of the tangents to the curve x^2+3x-2y^2=4 at the points where the curve crosses the x- axis

More Similar Questions