Posted by Matteo on Monday, March 7, 2011 at 3:53pm.
A curve has implicit equation x^22xy+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 xaxis.
b)Find the equation of the normal to the curve at the point (2sqrt3,sqrt3).

math  Reiny, Monday, March 7, 2011 at 5:29pm
x^22xy+4y^2=12
2x  2x dy/dx  2y + 8y^ dy/dx = 0
dy/dx(8y^2  2x) = 2y  2x
dy/dx = (yx)/(4y^2x)
to be horizontal to the xaxis, the slope must be zero, that is, dy/dx = 0
so yx = 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 )
Answer This Question
Related Questions
 Calculus  Maths  I got a few questions. Hope ya'll can help out. 1) for F(X...
 12th Grade Calculus  1. a.) Find an equation for the line perpendicular to the ...
 calculus  1. Given the curve a. Find an expression for the slope of the curve ...
 Ap calc.. Dying!! Please help!  Given the curve x^2xy+y^2=9 A) write a general...
 Calculus  The line that is normal to the curve x^2=2xy3y^2=0 at(1,1) ...
 calculus  A curve passes through the point (1,11) and it's gradient at any ...
 calculus  Consider the curve defined by 2y^3+6X^2(y) 12x^2 +6y=1 . a. Show ...
 calculus  there are two tangents lines to the curve f(x) = 3x^2 that pass ...
 Math Calculus (ALEVEL)  Find the equation of the tangents to the curve x^2+3x...
 Math, Calc  Use implicit differentiation to find an equation of the tangent ...
More Related Questions