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# core 4 implicit watch

1. The 2 points on the curve x^2 + y^2 - xy = 84 where the gradient of the curve is 1/3 are A and B. Find the eqns of the tangents at A and B.

my method was:

1) differentiate
2) sub 1/3 into dy/dx found in the implicit eqn.
3) use this to find the value of x and y
4) then finding the tangent for these values

Not getting the right answer? Any idea why?
2. (Original post by A*my)
The 2 points on the curve x^2 + y^2 - xy = 84 where the gradient of the curve is 1/3 are A and B. Find the eqns of the tangents at A and B.

my method was:

1) differentiate
2) sub 1/3 into dy/dx found in the implicit eqn.
3) use this to find the value of x and y
4) then finding the tangent for these values

Not getting the right answer? Any idea why?
2) Give a relationship between x and y, 5x=y.

Subbing back into the orginal equation gives two possible values for x, +/-2.

Sub each into original gives 4 possible points.

Check each for correct gradient, leaves (2,10), and (-2,-10).

Then work out tangents.

Probably an arithmetic slip on your part assuming the given answer is correct.

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Updated: November 11, 2017
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