Pure maths A-Level questions, HW, help

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anya2003
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Hi there, struggling with part b) can do part a) successfully but would appreciate some help after. Will attach Q in a sec.
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anya2003
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nikki.maria
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yeah lmao sure this is hw
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davros
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(Original post by anya2003)
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This question has been posted recently by someone else

At P (and Q) the tangent is vertical - what implication does this have for the denominator of dy/dx?
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anya2003
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(Original post by nikki.maria)
yeah lmao sure this is hw
shush shush
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anya2003
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(Original post by davros)
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At P (and Q) the tangent is vertical - what implication does this have for the denominator of dy/dx?
It will have ti equal 0, but you have 2 unknowns so not sure what to do next
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davros
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(Original post by anya2003)
It will have ti equal 0, but you have 2 unknowns so not sure what to do next
So if the denominator equals 0 you have an equation relating x and y. Write one variable in terms of the other, substitute into the original equation of the curve and that will give you a quadratic in x (or y) that you can solve to find possible coordinates for P (one solution will give you Q so check which one you want).
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anya2003
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(Original post by davros)
So if the denominator equals 0 you have an equation relating x and y. Write one variable in terms of the other, substitute into the original equation of the curve and that will give you a quadratic in x (or y) that you can solve to find possible coordinates for P (one solution will give you Q so check which one you want).
Thank you! It always sounds so much easier when someone else explains it to you haha.
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MiladA
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(Original post by anya2003)
It will have ti equal 0, but you have 2 unknowns so not sure what to do next
The tangent at P and Q is parallel to the Y axis. This means that the change in X is zero i.e. dx is 0. In other words X remains constant at P and Q (as it's a straight line). Use this information in your dy/dx and get an equation in terms of x and y, write x or y as the subject and substitute in equation of curve as you know that x (or y) will take that particular value at P and Q.

The same can be said if the tangent is parallel to the X axis then you would set dy=0 and do similar things.
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davros
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(Original post by MiladA)
The tangent at P and Q is parallel to the Y axis. This means that the change in X is zero i.e. dx is 0. In other words X remains constant at P and Q (as it's a straight line). Use this information in your dy/dx and get an equation in terms of x and y, write x or y as the subject and substitute in equation of curve as you know that x (or y) will take that particular value at P and Q.

The same can be said if the tangent is parallel to the X axis then you would set dy=0 and do similar things.
Please no!

dy/dx is not a fraction. You are not setting dx = 0 or dy = 0, you are setting the numerator or denominator of dy/dx to zero, corresponding to a vertical or horizontal tangent respectively
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