Category: Coordinate Geometry

Question Number 128611 by malwan last updated on 08/Jan/21 $${write}\:{the}\:{equation}\:{of}\:{the}\: \\ $$$${circle}\:{which}\:{containing}\: \\ $$$${the}\:{points}\:\left(\mathrm{4},−\mathrm{3}\right),\left(\mathrm{1},−\mathrm{2}\right) \\ $$$${and}\:{center}\:{on}\:{line} \\ $$$$\mathrm{3}{x}\:+\:\mathrm{4}{y}\:=\mathrm{7} \\ $$ Answered by mr W last…

Question Number 62938 by ajfour last updated on 27/Jun/19 Commented by ajfour last updated on 27/Jun/19 $${Question}\:\mathrm{62861}\:\left({revisit}\right) \\ $$ Answered by ajfour last updated on…

Question Number 128303 by mr W last updated on 06/Jan/21 Commented by mr W last updated on 06/Jan/21 $${find}\:{side}\:{length}\:{s}\:{of}\:{the}\:{equilateral} \\ $$$${triangle}\:{ABC}\:{in}\:{terms}\:{of}\:{radii}\:{R} \\ $$$${and}\:{r}. \\ $$…

Question Number 62753 by peter frank last updated on 24/Jun/19 $${The}\:{normal}\:{at}\:{the}\:{point} \\ $$$${P}\left(\mathrm{4cos}\:\theta,\mathrm{3sin}\:\theta\right)\:{on}\:{the} \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{\mathrm{16}}\:+\frac{{y}^{\mathrm{2}} }{\mathrm{9}}=\mathrm{1}\:{meets} \\ $$$${the}\:{x}−{axis}\:{and}\:{y}−{axis} \\ $$$${at}\:{A}\:{and}\:{B}\:{respectively} \\ $$$${show}\:{that}\:{locus}\:{of}\:{the} \\ $$$${mid}−{point}\:{of}\:{AB}\:{is}\:{an}…

Question Number 127509 by mr W last updated on 30/Dec/20 Commented by mr W last updated on 31/Dec/20 $${if}\:{both}\:{ellipses}\:{have}\:{the}\:{same}\:{shape} \\ $$$${as}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1},\:{determine}\:\frac{{b}}{{a}}=?…