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Category: Coordinate Geometry

in-what-ratio-in-which-y-x-2-0-divides-the-line-joining-3-1-and-8-9-

Question Number 25441 by rather ishfaq last updated on 10/Dec/17 $${in}\:{what}\:{ratio}\:{in}\:{which}\:{y}−{x}+\mathrm{2}=\mathrm{0}\:{divides}\:{the}\:{line}\:{joining}\:\left(\mathrm{3},−\mathrm{1}\right)\:{and}\:\left(\mathrm{8},\mathrm{9}\right). \\ $$$$ \\ $$ Answered by mrW1 last updated on 10/Dec/17 $${Line}\:{from}\:{A}\left(\mathrm{3},−\mathrm{1}\right)\:{to}\:{B}\left(\mathrm{8},\mathrm{9}\right): \\ $$$$\left({x},{y}\right)=\left(\mathrm{3},−\mathrm{1}\right)+\lambda\left(\mathrm{5},\mathrm{10}\right)…

Question-25201

Question Number 25201 by tawa tawa last updated on 06/Dec/17 Answered by ajfour last updated on 06/Dec/17 $${y}=\frac{\mathrm{6}}{\mathrm{3}{x}−\mathrm{2}}\:\:\:\Rightarrow\:\:\frac{{dy}}{{dx}}\mid_{{x}=\mathrm{2}} =−\frac{\mathrm{18}}{\left(\mathrm{3}{x}−\mathrm{2}\right)^{\mathrm{2}} }\mid_{{x}=\mathrm{2}} \\ $$$$\:\:\:\frac{{dy}}{{dx}}\mid_{{x}=\mathrm{2}} =−\frac{\mathrm{9}}{\mathrm{8}}\:. \\ $$$${V}=\int_{\mathrm{1}}…

The-point-A-has-coordinate-1-5-and-the-point-B-has-coordinates-7-1-The-perpendicular-bisector-of-AB-meets-the-x-axis-at-C-and-the-y-axis-at-D-Calculate-the-length-of-CD-

Question Number 25200 by tawa tawa last updated on 06/Dec/17 $$\mathrm{The}\:\mathrm{point}\:\mathrm{A}\:\mathrm{has}\:\mathrm{coordinate}\:\left(−\:\mathrm{1},\:\:−\:\mathrm{5}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{point}\:\mathrm{B}\:\mathrm{has}\:\mathrm{coordinates}\:\left(\mathrm{7},\:\mathrm{1}\right). \\ $$$$\mathrm{The}\:\mathrm{perpendicular}\:\mathrm{bisector}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{meets}\:\mathrm{the}\:\mathrm{x}\:−\:\mathrm{axis}\:\mathrm{at}\:\mathrm{C}\:\mathrm{and}\:\mathrm{the}\:\mathrm{y}\:−\:\mathrm{axis}\:\mathrm{at} \\ $$$$\mathrm{D}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{CD} \\ $$ Answered by mrW1 last updated on 06/Dec/17 $${Middle}\:{of}\:{AB}={M}\left(\frac{−\mathrm{1}+\mathrm{7}}{\mathrm{2}},\frac{−\mathrm{5}+\mathrm{1}}{\mathrm{2}}\right)={M}\left(\mathrm{3},−\mathrm{2}\right)…

A-line-has-equation-y-2x-7-and-a-curve-has-equation-y-x-2-4x-c-where-c-is-a-constant-Find-the-set-of-possible-values-of-c-for-which-the-line-does-not-intersect-the-curve-

Question Number 25199 by tawa tawa last updated on 06/Dec/17 $$\mathrm{A}\:\mathrm{line}\:\mathrm{has}\:\mathrm{equation}\:\mathrm{y}\:=\:\mathrm{2x}\:−\:\mathrm{7}\:\mathrm{and}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{has}\:\mathrm{equation}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{c}, \\ $$$$\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{c}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{intersect}\:\mathrm{the}\:\mathrm{curve}. \\ $$ Commented by tawa tawa last updated on…