I was trying ( unsuccessfully ) to find the minimum distance between two parabolas and thought that I could do that by finding the minimum distance between two parallel tangents to the two parabolas. However there comes a case when ( as shown in figure ) the tangents are indeed parallel and the distance between them is also minimum but ( as shown by the green line ) the actual distance between the point of contacts is not the distance between the parallel lines but much more ... How do I do such problems ??

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TopNewestMinimum distance will be along common normal. Use little calculus & co-ordinate geometry to get it. – Piyushkumar Palan · 3 years, 9 months ago

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– Tanya Gupta · 3 years, 5 months ago

I don't think calculus will be needed....work using the parabola y^2=4ax....and use the parametric form of the equation i.e. (at^2,2at)...then write equation for both the normals and equate them....works beautifully!!!Log in to reply

– Devkant Chouhan · 9 months, 3 weeks ago

How can we equate them there would be two variable t1 and t2Log in to reply

You can find the symmetry line.......as an example y=x is the line of symmetry between y^2=4x and x^2=4y double the dist from one parabola to y=x and you get the distance – Saswata Dasgupta · 2 years, 3 months ago

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Ooh! My favorite! You have to set up a distance formula, with each equation as a point! It's awesome! From there, you simplify, and use basic algebra to minimize! Great post! – Finn Hulse · 3 years, 5 months ago

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cool – Jafar Badour · 2 years, 5 months ago

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can be solved by making the equation in a variable involving parametric equations for the two curves .. try to get it in one single parameter and then differentiate to get the critical point.. !! – Ramesh Goenka · 3 years, 9 months ago

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lagrange methode in calculus maybe help – Abdul Siregar · 3 years, 9 months ago

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