Menu Close

Category: Coordinate Geometry

An-equilateral-triangle-inscribed-in-a-parabola-y-2-4x-One-of-its-vertices-is-at-the-vertex-of-the-parabola-Find-the-length-of-each-side-of-the-triangle-in-units-

Question Number 201660 by LimPorly last updated on 10/Dec/23 $${An}\:{equilateral}\:{triangle}\:{inscribed}\:{in}\:{a}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}.\:{One}\:{of}\:{its}\:{vertices}\:{is}\:{at}\:{the}\:{vertex}\:{of}\:\:{the}\:{parabola}. \\ $$$${Find}\:{the}\:{length}\:{of}\:{each}\:{side}\:{of}\:{the}\:{triangle}\:{in}\:{units}. \\ $$ Answered by som(math1967) last updated on 10/Dec/23 $$\:{slope}\:{of}\:{AB}\:={tan}\mathrm{30}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}…

Find-the-shortest-distance-between-point-A-3-2-and-curve-y-x-x-gt-0-

Question Number 201659 by LimPorly last updated on 10/Dec/23 $${Find}\:{the}\:{shortest}\:{distance}\:{between}\: \\ $$$${point}\:{A}\left(\mathrm{3},\mathrm{2}\right)\:{and}\:{curve}\:{y}=\sqrt{{x}}\:\left({x}>\mathrm{0}\right). \\ $$ Answered by mr W last updated on 10/Dec/23 $${say}\:{the}\:{distance}\:{is}\:{s}. \\ $$$${say}\:{the}\:{point}\:{on}\:{the}\:{curve}\:{is}\:\left({p}^{\mathrm{2}}…