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Category: Coordinate Geometry

the-line-x-y-2-cuts-a-circle-x-2-y-2-4-at-two-points-find-the-co-ordinates-of-points-

Question Number 29365 by gyugfeet last updated on 08/Feb/18 $${the}\:{line}\:{x}+{y}=\mathrm{2}\:{cuts}\:{a}\:{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}\:} =\mathrm{4}\:{at}\:{two}\:{points}.\:{find}\:{the}\:{co}−{ordinates}\:{of}\:{points}. \\ $$ Answered by Rasheed.Sindhi last updated on 08/Feb/18 $$\begin{cases}{{x}+{y}=\mathrm{2}}\\{{x}^{\mathrm{2}} +{y}^{\mathrm{2}\:} =\mathrm{4}}\end{cases}\Rightarrow\begin{cases}{{y}=\mathrm{2}−{x}}\\{{x}^{\mathrm{2}} +\left(\mathrm{2}−{x}\right)^{\mathrm{2}}…

Question-29332

Question Number 29332 by Tinkutara last updated on 07/Feb/18 Answered by ajfour last updated on 07/Feb/18 $${let}\:{eq}.\:{of}\:{circle}\:{be} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{gx}+\mathrm{2}{fy}=\mathrm{0}\:\:\:\:\:\left({c}=\mathrm{0}\right) \\ $$$${for}\:{two}\:{circles}\:{to}\:{cut}\:{orthogonally} \\ $$$$\:\:\:\mathrm{2}{g}_{\mathrm{1}}…

if-the-x-a-y-b-1-passes-through-the-point-lf-intersection-of-the-lines-x-y-3-and-2x-3y-1-and-is-parallel-to-the-line-y-x-6-then-find-the-value-of-a-and-b-

Question Number 29276 by gyugfeet last updated on 06/Feb/18 $${if}\:{the}\:\frac{{x}}{{a}}+\frac{{y}}{{b}}=\mathrm{1}\:{passes}\:{through}\:{the}\:{point}\:{lf}\:{intersection}\:{of}\:{the}\:{lines}\:{x}+{y}=\mathrm{3}\:{and}\:\mathrm{2}{x}−\mathrm{3}{y}=\mathrm{1}\:{and}\:{is}\:{parallel}\:{to}\:{the}\:{line}\:{y}={x}−\mathrm{6}\:{then}\:{find}\:\:{the}\:{value}\:{of}\:{a}\:\:{and}\:{b}.\: \\ $$ Answered by Rasheed.Sindhi last updated on 06/Feb/18 $$\mathrm{Intersection}\:\mathrm{point}\:\mathrm{of}\:{x}+{y}=\mathrm{3}\:{and}\:\mathrm{2}{x}−\mathrm{3}{y}=\mathrm{1} \\ $$$${y}=\mathrm{3}−{x}\:\Rightarrow\mathrm{2}{x}−\mathrm{3}\left(\mathrm{3}−{x}\right)=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\mathrm{2}\:,\:{y}=\mathrm{1} \\…

Question-160333

Question Number 160333 by cortano last updated on 27/Nov/21 Commented by blackmamba last updated on 28/Nov/21 $$\:\left(\ast\right){r}\::\:{y}={mx}+\mathrm{3} \\ $$$$\left(\ast\ast\right){s}:\:{y}={px}+\mathrm{3} \\ $$$$\:\left(\ast\ast\ast\right)\:{gradien}\:={y}'={m} \\ $$$$\:\:\mathrm{8}{x}−\mathrm{2}{yy}'\:=\:\mathrm{0}\Rightarrow{y}'=\frac{\mathrm{4}{x}}{{y}}\:\wedge\:{m}=\frac{{y}−\mathrm{3}}{{x}} \\ $$$$\:\Rightarrow\frac{\mathrm{4}{x}}{{y}}=\frac{{y}−\mathrm{3}}{{x}}\:;\:\mathrm{4}{x}^{\mathrm{2}}…

Question-29231

Question Number 29231 by Tinkutara last updated on 05/Feb/18 Answered by ajfour last updated on 05/Feb/18 $${eq}.\:{of}\:{chord}\:{of}\:{contact}\:{to}\:{circle} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} =\mathrm{1}\:\:\:{from}\:\:\left({x}_{\mathrm{1}} ,\:{y}_{\mathrm{1}} \right)\:\:{is} \\ $$$${xx}_{\mathrm{1}}…

find-the-area-and-perimeter-of-x-a-2-3-y-b-2-3-1-

Question Number 159958 by mr W last updated on 22/Nov/21 $${find}\:{the}\:{area}\:{and}\:{perimeter}\:{of} \\ $$$$\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{a}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\frac{\boldsymbol{{y}}}{\boldsymbol{{b}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{1} \\ $$ Commented by MJS_new last updated on 23/Nov/21 $${y}=\pm\frac{{b}}{{a}}\left({a}^{\mathrm{2}/\mathrm{3}}…