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Category: Coordinate Geometry

Question-52731

Question Number 52731 by ajfour last updated on 12/Jan/19 Commented by MJS last updated on 12/Jan/19 $$\mathrm{for}\:{b}={a}\:\left(\mathrm{circle}\right)\:\mathrm{the}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{one}\:\mathrm{with}\:\mathrm{minimum}\:\mathrm{perimeter}. \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{draw}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{for}\:\mathrm{a} \\ $$$$\mathrm{circle}\:\mathrm{with}\:{r}={a}\:\mathrm{and}\:\mathrm{then}\:\mathrm{compress}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{factor}\:\frac{{a}}{{b}}\:\left[{P}=\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:\rightarrow\:{P}'=\begin{pmatrix}{{x}}\\{\frac{{b}}{{a}}{y}}\end{pmatrix}\right]…

Question-52558

Question Number 52558 by ajfour last updated on 09/Jan/19 Commented by ajfour last updated on 10/Jan/19 $${eq}.\:{of}\:{parabola}\:{be}\:{y}=\:\frac{{x}^{\mathrm{2}} }{{a}}\:\:{and} \\ $$$${eq}.\:{of}\:{line}\:\:{be}\:{y}=\:{mx}\:\:\:\left({m}=\mathrm{tan}\:\phi\right), \\ $$$${if}\:{both}\:{circles}\:{touch}\:{the}\:{line}\:{at}\:{a} \\ $$$${same}\:{point}\:{and}\:{circle}\:{in}\:{red}\:{has} \\…