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For the parabola \(x^2+4y^2-4xy-10x+5=0\), find the equation of tangent at vertex and equation of axis of parabola?

Note by Advitiya Brijesh
4 years ago

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This is an interesting problem, namely because the parabola's axis is not parallel to an x-y axis. We are used to dealing with conics in this form. However, using the definition of a parabola (distance to a point on the parabola is the same from a fixed point called the focus and a fixed line called the directrix), one can develop a hairy formula for a general parabola. Plugging in and solving for some variables, I got a possible focus to be (1,0) and a possible directrix of x-2y=0. The axis of the parabola then must be 2x+y=2, and the vertex (9/10,7/10). There could be more answers, but I didn't check. If you want me to look more into this problem or write a formal proof, I'll consider it. Bob Krueger · 4 years ago

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your in level four of geometry...please give it a try at least....it does not need much perspiration...best of luck ....:) Raja Metronetizen · 4 years ago

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@Raja Metronetizen Dude this is already done... but i liked this problem very much that's why posted that.. Advitiya Brijesh · 4 years ago

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