The Student Room Group
fallen_star
1)the curve c has equation
13x² +13y² - 10xy = 52

find the dy/dx as a function of x and y, simplifying the answer


2) a curve has equation 7x² +48xy - 7y² +75 =0
a and b are 2 distinct points on the curve. at each of these points the gradient of the curve is equal to 2/11.
a) find the implicit differentiation to show that x + 2y = 0 at the points a and b
b) find the co-ordinates of the points a and b


26x+26y(dy/dx)-10y-10x(dy/dx)=0
2(dy/dx)(13y-5x)=2(5y-13x)
dy/dx=(5y-13x)/(13y-5x)

2.
a)
14x+48y+48x(dy/dx)-14y(dy/dx)=0
dy/dx=(14x+48y)/(14y-48x)=(7x+24y)/(7y-24x)

2/11=(7x+24y)/(7y-24x)
14y-48x=77x+264y
0=125x+250y
so x+2y=0

b) x=-2y substitute into equation of curve:

28y² -96y² - 7y² +75 =0
75y²-75=0
y²-1=0
y=±1 and then use x=-2y

so (-2,1) and (2,-1)
Reply 2
fallen_star
1)


I see I have been beaten by wacabac...pleased that our solutions agree.
steve2005
I see I have been beaten by wacabac...pleased that our solutions agree.


just curious what programme you use to write maths in as a need a good one, as want to transfer some notes onto my computer.
Reply 4
pratikv
just curious what programme you use to write maths in as a need a good one, as want to transfer some notes onto my computer.


Typing program is MathType which is an upgrade from Equation Editor which is a free program available on most PC's.

Search on your computer for "Equation" with luck you will find a folder, inside which is an icon


Equation Editor can also be found in Word <Insert<Object<Equation

http://www.mathtype.com/en/products/mathtype/
steve2005
Typing program is MathType which is an upgrade from Equation Editor which is a free program available on most PC's.

Search on your computer for "Equation" with luck you will find a folder, inside which is an icon


Equation Editor can also be found in Word <Insert<Object<Equation

http://www.mathtype.com/en/products/mathtype/


cheers. :biggrin: