Posted by Matteo on Monday, March 7, 2011 at 3:53pm.
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 - Reiny, Monday, March 7, 2011 at 5:29pm
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 )
Answer This Question
More 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^2-xy+y^2=9 A) write a general...
- Calculus - The line that is normal to the curve x^2=2xy-3y^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 ...