Category: Coordinate Geometry

Question Number 9732 by tawakalitu last updated on 29/Dec/16 $$\mathrm{Find}\mathrm{equation}\mathrm{of}\mathrm{an}\mathrm{ellipse}\mathrm{whose}\mathrm{major}\mathrm{axis}$$$$\mathrm{is}\mathrm{vertical},\mathrm{with}\mathrm{the}\mathrm{center}\mathrm{located}(-1,3)$$$$\mathrm{at}\mathrm{the}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{center}\mathrm{and}\mathrm{one}$$$$\mathrm{of}\mathrm{the}\mathrm{covertices}\mathrm{equal}\mathrm{to}4,\mathrm{and}\mathrm{the}\mathrm{distance}$$$$\mathrm{between}\mathrm{the}\mathrm{center}\mathrm{and}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{vertices}$$$$\mathrm{equal}\mathrm{to}6.$$ Answered by sandy_suhendra…

Question Number 9163 by tawakalitu last updated on 21/Nov/16 $$\mathrm{show}\mathrm{that}\mathrm{the}\mathrm{ellipse}\mathrm{with}\mathrm{e}=\frac{\sqrt{5}}{3},$$$$\mathrm{focus}(0,2)\mathrm{and}\mathrm{directrix}\mathrm{x}=-\frac{4\sqrt{5}}{3}$$$$\mathrm{has}\mathrm{the}\mathrm{equation}:\frac{{(\mathrm{x}-\sqrt{5})}^2}{9}+\frac{{(\mathrm{y}-2)}^2}{4}=1$$ Commented by sandy_suhendra last updated on 22/Nov/16…

Question Number 74649 by ajfour last updated on 28/Nov/19 Commented by ajfour last updated on 28/Nov/19 $$Find{\theta }_{max}intermsofa,b,c.$$$$Theboundaryisanellipse.$$ Answered by ajfour…

Question Number 8929 by kuldeep singh raj last updated on 06/Nov/16 Commented by Rasheed Soomro last updated on 06/Nov/16 $$\mathrm{This}\mathrm{depends}\mathrm{upon}\mathrm{the}\mathrm{position}\mathrm{of}\mathrm{C}.$$$$\mathrm{For}\mathrm{example}\mathrm{how}\mathrm{far}\mathrm{is}\mathrm{C}\mathrm{from}\mathrm{A}.$$$$\mathrm{So}\:\mathrm{additional}\:\:\mathrm{information}\:\mathrm{is}\:\mathrm{required} \…

Question Number 74300 by ~blr237~ last updated on 21/Nov/19 $$Letconsider\gamma :I\to {\mathbb{R}}^{2}aparametriccurve$$$$1)Provethatifa<band\gamma \left(a\right)\ne \gamma \left(b\right)thenthereexist{t}_0\in ]a,b[$$$$suchas{\gamma }^{\prime }\left(t_0\right)iscolinearto\gamma \left(b\right)-\gamma \left(a\right)$$$$2)Showthatif\gamma isregularandthefunctionf:I\to \mathbb{R}t\to f\left(t\right)=\mid \mid \gamma \left(t\right)-O(0,0)\mid \mid ismaximalin{t}_0\in I$$$${Then}\:\:\mid{K}_{\gamma} \left({t}_{\mathrm{0}} \right)\mid\geqslant\frac{\mathrm{1}}{{f}\left({t}_{\mathrm{0}} \right)}…