Parametric equations help! Watch

Student10011
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So let's say I have the equation xy=c^2,with a general point p(ct,c/t), where c is a constant.

Obviously the value of t can vary for the set of parametric equations. But when we find a tangent to the general point on P, say we get t^2-10ct-5=0) surely the value of t for this equation becomes a constant, since this tangent is a cartesian equation?

If that's right, let me know, if not please correct me,

thanks!
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davros
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(Original post by Student10011)
So let's say I have the equation xy=c^2,with a general point p(ct,c/t), where c is a constant.

Obviously the value of t can vary for the set of parametric equations. But when we find a tangent to the general point on P, say we get t^2-10ct-5=0) surely the value of t for this equation becomes a constant, since this tangent is a cartesian equation?

If that's right, let me know, if not please correct me,

thanks!
Not really sure what you're asking here!

t is a parameter , which means that as its value varies you get a different point on the curve.

At a general point (ct, c/t) the equation of the tangent wil depend on t, but as t changes (and the point moves around the curve) the equation of the tangent will change too!
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TenOfThem
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(Original post by Student10011)
So let's say I have the equation xy=c^2,with a general point p(ct,c/t), where c is a constant.

Obviously the value of t can vary for the set of parametric equations. But when we find a tangent to the general point on P, say we get t^2-10ct-5=0) surely the value of t for this equation becomes a constant, since this tangent is a cartesian equation?

If that's right, let me know, if not please correct me,

thanks!
t does not become a constant but you can find the value of t at the point of interest
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brianeverit
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(Original post by Student10011)
So let's say I have the equation xy=c^2,with a general point p(ct,c/t), where c is a constant.

Obviously the value of t can vary for the set of parametric equations. But when we find a tangent to the general point on P, say we get t^2-10ct-5=0) surely the value of t for this equation becomes a constant, since this tangent is a cartesian equation?

If that's right, let me know, if not please correct me,

thanks!
I don;t know where you have got t^2-10ct-5=0 from. The equation of tangent at (ct,c/t) is t^2y=-x+2ct
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