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Category: Coordinate Geometry

Question-28565

Question Number 28565 by ajfour last updated on 27/Jan/18 Answered by ajfour last updated on 27/Jan/18 $${eq}.\:{of}\:{tangents}\:{through}\:{P}\left({h},{k}\right) \\ $$$$\:\:\:{y}−{k}\:=\:{m}\left({x}−{h}\right) \\ $$$${applying}\:{condition}\:{for}\:{tangency}: \\ $$$$\left({k}−{mh}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} {m}^{\mathrm{2}}…

Question-28512

Question Number 28512 by ajfour last updated on 26/Jan/18 Commented by ajfour last updated on 26/Jan/18 $${If}\:{eq}.\:{of}\:{line}\:{AB}\:{is}\:\boldsymbol{{y}}=\boldsymbol{{mx}}+\boldsymbol{{c}} \\ $$$${and}\:{that}\:{of}\:{ellipse}\:{is}\:\:\frac{\boldsymbol{{x}}^{\mathrm{2}} }{\boldsymbol{{a}}^{\mathrm{2}} }+\frac{\boldsymbol{{y}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} }=\mathrm{1}\:, \\ $$$${find}\:{eq}.\:{of}\:{circle}\:{with}\:{AB}\:{as}…

Find-the-direction-cosines-of-two-lines-which-are-connected-by-relation-l-m-n-0-mn-2nl-2lm-0-my-solution-l-m-n-mn-2n-m-n-2-n-m-n-0-2m-2-5mn-2n-2-0-2m-n-m-2n-0-m-2n-or-m-1-2-n-case-1-m-

Question Number 28504 by rish@bh last updated on 26/Jan/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{cosines}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{lines}\:\mathrm{which}\:\mathrm{are}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{relation} \\ $$$${l}+{m}+{n}=\mathrm{0} \\ $$$${mn}−\mathrm{2}{nl}−\mathrm{2}{lm}=\mathrm{0} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{my}}\:\boldsymbol{\mathrm{solution}} \\ $$$${l}=−\left({m}+{n}\right) \\ $$$${mn}+\mathrm{2}{n}\left({m}+{n}\right)+\mathrm{2}\left({n}+{m}\right){n}=\mathrm{0} \\…

Question-28411

Question Number 28411 by ajfour last updated on 25/Jan/18 Commented by ajfour last updated on 25/Jan/18 $${The}\:{smaller}\:{sphere}\:{touches}\:{the} \\ $$$${paraboloid}\:{only}\:{at}\:{inner}\:{bottommost}, \\ $$$${point}.\:{Find}\:{the}\:{smallest}\:{value} \\ $$$${of}\:\boldsymbol{{R}}\:{in}\:{terms}\:{of}\:\boldsymbol{{r}},\:{if}\:{the}\:{larger} \\ $$$${sphere}\:{touches}\:{the}\:{smaller}\:{sphere}…

Question-28384

Question Number 28384 by ajfour last updated on 25/Jan/18 Answered by ajfour last updated on 25/Jan/18 $${If}\:{new}\:{coordinate}\:{axes}\:{be} \\ $$$${tangent}\:{at}\:{A}\:\left({towards}\:{right}\right) \\ $$$${x}\:{axis}\:{and}\:{axis}\:{of}\:{parabola}\:{the} \\ $$$${y}\:{axis}\:\left({upwards}\right),\:{then}\:{eq}.\:{of} \\ $$$${parabola}\:{is}\:\:\boldsymbol{{y}}=\boldsymbol{{px}}^{\mathrm{2}}…

At-what-point-of-the-parabola-y-x-2-will-the-tangent-a-be-parallel-to-the-line-y-4x-5-b-be-perpendicular-to-2x-6y-5-0-c-make-an-angle-of-45-with-3x-y-1-0-

Question Number 93855 by Ar Brandon last updated on 15/May/20 $$\mathrm{At}\:\mathrm{what}\:\mathrm{point}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parabola}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{will}\:\mathrm{the}\:\mathrm{tangent}\: \\ $$$$\mathrm{a}\backslash\:\mathrm{be}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}=\mathrm{4x}−\mathrm{5} \\ $$$$\mathrm{b}\backslash\:\mathrm{be}\:\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{2x}−\mathrm{6y}+\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{c}\backslash\:\mathrm{make}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}^{°} \:\mathrm{with}\:\mathrm{3x}−\mathrm{y}+\mathrm{1}=\mathrm{0} \\ $$ Answered by Kunal12588…