GilbertKeithChesterton
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- Jun 15, 2020
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Question is from Schaum's Guide to Calculus, p.97 q.18:
For the ellipse [MATH][/MATH][MATH]b^2x^2+a^2y^2=a^2b^2[I][/I][/MATH] show that the equations of its tangent lines of slope m are [MATH]y=mx \pm \sqrt{a^2m^2+b^2}[/MATH]
Question is in chapter on tangent lines and is mostly based on taking implicit derivatives and plugging into point-slope format for the tangent lines. I've seen complicated derivations based on substituting mx+c into the ellipse question and solving for c (by setting the discriminant of the quadratic to zero) but I'm 99.999% certain the book isn't asking for this as that would be far more complex than anything yet covered up to this point.
Really appreciate any help anyone can offer here!
Andrew
For the ellipse [MATH][/MATH][MATH]b^2x^2+a^2y^2=a^2b^2[I][/I][/MATH] show that the equations of its tangent lines of slope m are [MATH]y=mx \pm \sqrt{a^2m^2+b^2}[/MATH]
Question is in chapter on tangent lines and is mostly based on taking implicit derivatives and plugging into point-slope format for the tangent lines. I've seen complicated derivations based on substituting mx+c into the ellipse question and solving for c (by setting the discriminant of the quadratic to zero) but I'm 99.999% certain the book isn't asking for this as that would be far more complex than anything yet covered up to this point.
Really appreciate any help anyone can offer here!
Andrew