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C4 Implicit diffrentiation help please

I cant seem to do this question, help appreciated...

its from elmwood paper C4 B, Question 1 , from free exam papers.com

a)find the gradient of the line with equation
(x-2)(y+5)=12

b)find the eqn of the normal at point (4,1)

when i did it i got
(-5-y)/(x-2) for part a

but the answer in mrskscheme is (y+5)/(2-x)
I dont understand why my signs are wrong, seem to make this mistake again and again, dont quite know why....
help please:s-smilie: thanks
(edited 13 years ago)
Reply 1
Avatar for Swayum
Swayum
18
Original post by hazu121
I cant seem to do this question, help appreciated...

its from elmwood paper C4 B, Question 1 , from free exam papers.com

a)find the gradient of the line with equation
(x-2)(y-3)=12

b)find the eqn of the normal at point (4,1)

when i did it i got
(-5-y)/(x-2) for part a

but the answer in mrskscheme is (y+5)/(2-x)
I dont understand why my signs are wrong, seem to make this mistake again and again, dont quite know why....
help please:s-smilie: thanks


(-5-y)(x-2) = (y+5)/(2-x), just factorise the -1 from the numerator and multiply it into the denominator.

However, (x-2)(y-3)=12 is not a line. Also, I have no clue where you're getting (y+5)/(2-x) from really.
Reply 2
Avatar for hazu121
hazu121
OP
Original post by Swayum
(-5-y)(x-2) = (y+5)/(2-x), just factorise the -1 from the numerator and multiply it into the denominator.

However, (x-2)(y-3)=12 is not a line. Also, I have no clue where you're getting (y+5)/(2-x) from really.


Hey thanks, for the speedy reply :smile:
Sorry I just realised that I made a mistake in the original post, should be (x-2)(y+5)=12
also, Im not sure what you mean
if you factorise -1 from the numerator it would be -1(y+5) /(x-2)
how do you then multiply it into the denominator, are you allowed to do that?
(edited 13 years ago)
Reply 3
Avatar for Swayum
Swayum
18
Yes, of course.

−35=3−5=−0.6\frac{-3}{5} = \frac{3}{-5} = -0.6

It works because -1 * -1 = 1, so rearranging gives -1 = 1/-1. And also -1 * 1 = -1, so rearranging gives -1 = -1/1. Put the two together and you get

-1 = 1/-1 = -1/1 (which means you can put the minus sign anywhere, numerator or denominator)
(edited 13 years ago)
Reply 4
Avatar for hazu121
hazu121
OP
Original post by Swayum
Yes, of course.

−35=3−5=−0.6\frac{-3}{5} = \frac{3}{-5} = -0.6

It works because -1 * -1 = 1, so rearranging gives -1 = 1/-1. And also -1 * 1 = -1, so rearranging gives -1 = -1/1. Put the two together and you get

-1 = 1/-1 = -1/1 (which means you can put the minus sign anywhere, numerator or denominator)


Ok, I thought so...
but does that mean that either answer is accepted, though the markscheme one is seen as more acceptable as it is neater?
Sorry, it seems quite simple now :biggrin:
Reply 5
Avatar for Swayum
Swayum
18
Original post by hazu121
Ok, I thought so...
but does that mean that either answer is accepted, though the markscheme one is seen as more acceptable as it is neater?
Sorry, it seems quite simple now :biggrin:


Yes, either would be fine.

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