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C4 implicit

At what points are the tangents to the circle x^2+y^2-6y-8x=0 parallel to the y-axis?

i differentiated the equation and got:

2x + 2ydy/dx - 6dy/dx -8

then my gradient equals this: 8-2x/2y-6

now what do i do if i equal it to zero one of my co-ordinates my x coordinate will equal 4 and thats not in the answers.

thanks in advance, kind regards
(edited 12 years ago)
the first part is wrong it 2x+2ydy/dx not minus
You have an incorrect sign in your differentiated line and forgot = 0

You are not trying to find when dy/dx = 0

You are trying to find when the tangent is parallel to the y axis not the x axis
Reply 3
Avatar for BigBrain
BigBrain
You are trying to find when the line is parallel to the y axis so use dx/dy=0

so (2y-6)/(2x-8)=0

2y-6=0
y=3

When y=3, x^2-8x-9=0
so (x-9)(x+1)=0

voila :smile: (9,3) and (-1,3)

Are these right?
Reply 4
Avatar for kurdishboy94
kurdishboy94
OP
1
Original post by BigBrain
You are trying to find when the line is parallel to the y axis so use dx/dy=0

so (2y-6)/(2x-8)=0

2y-6=0
y=3

When y=3, x^2-8x-9=0
so (x-9)(x+1)=0

voila :smile: (9,3) and (-1,3)

Are these right?


yessss you genuissssss
Reply 5
Avatar for f1mad
f1mad
13
The gradient is undefined when denominator=0

dy/dx= (2x-8)/(2y-6)=0

Solve the denominator for 0.

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