Category: Coordinate Geometry

Question Number 6716 by Tawakalitu. last updated on 15/Jul/16 $${Prove}\:{that}\:{the}\:{locus}\:{of}\:{a}\:{point}\:{which}\:{moves}\:{its}\:{distance}\:{from}\: \\ $$$${the}\:{point}\:\left(−{b},\:\mathrm{0}\right)\:{is}\:{p}\:{times}\:{its}\:{distance}\:{from}\:{the}\:{point}\:\left({b},\:\mathrm{0}\right)\:{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({p}^{\mathrm{2}} \:−\:\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right)\:−\:\mathrm{2}{b}\left({p}^{\mathrm{2}} \:+\:\mathrm{1}\right){x}\:=\:\mathrm{0} \\ $$$${Show}\:{that}\:{this}\:{locus}\:{is}\:{a}\:{circle}\:{and}\:{find}\:{its}\:{radius}. \\ $$ Answered by…

Question Number 6681 by Tawakalitu. last updated on 11/Jul/16 Answered by Rasheed Soomro last updated on 12/Jul/16 $${Join}\:\mathrm{O}\:{and}\:\mathrm{Y}. \\ $$$$\because\:\:\mathrm{OX}=\mathrm{OY}=\mathrm{OZ}\:\:\left[{Radii}\:{of}\:{same}\:{circle}\right] \\ $$$$\therefore\:\bigtriangleup\mathrm{XOY}\:\:{and}\:\:\bigtriangleup\mathrm{ZOY}\:{are}\:{issoscel}\:{triangles}. \\ $$$$\therefore\:\:\angle\mathrm{XYO}=\angle\mathrm{OXY}=\mathrm{30}\:\:\:{and}\:\:\:\:\angle\mathrm{ZYO}=\angle\mathrm{OZY}=\mathrm{20} \\…

Question Number 137412 by oustmuchiya@gmail.com last updated on 02/Apr/21 Answered by herbert last updated on 02/Apr/21 $${gradient}\:{of}\:{l}_{\mathrm{1}} \:=\:\frac{\mathrm{2}+\mathrm{4}}{\mathrm{5}+\mathrm{1}}\:=\frac{\mathrm{6}}{\mathrm{6}}=\mathrm{1} \\ $$$${but}\:{grad}\:{of}\:{l}_{\mathrm{1}} ×{l}_{\mathrm{2}} =−\mathrm{1} \\ $$$${grad}\:{of}\:{l}_{\mathrm{2}} =−\mathrm{1}…

Question Number 6203 by sanusihammed last updated on 18/Jun/16 Answered by nburiburu last updated on 25/Jun/16 $${defining} \\ $$$${AC}={a} \\ $$$${AB}={b} \\ $$$${then} \\ $$$${BC}=\sqrt{{a}^{\mathrm{2}}…

Question Number 136781 by bramlexs22 last updated on 25/Mar/21 $$ \\ $$What is the equation of the circle passing though (-2,-4) and (4,6) its center…