Category: Coordinate Geometry

Question Number 28565 by ajfour last updated on 27/Jan/18 Answered by ajfour last updated on 27/Jan/18 $$eq.oftangentsthroughP(h,k)$$$$y-k=m(x-h)$$$$applyingconditionfortangency:$$$$\left({k}−{mh}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} {m}^{\mathrm{2}}…

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

Question Number 28411 by ajfour last updated on 25/Jan/18 Commented by ajfour last updated on 25/Jan/18 $$Thesmallerspheretouchesthe$$$$paraboloidonlyatinnerbottommost,$$$$point.Findthesmallestvalue$$$$of\mathit{R}intermsof\mathit{r},ifthelarger$$$${sphere}\:{touches}\:{the}\:{smaller}\:{sphere}…

Question Number 28384 by ajfour last updated on 25/Jan/18 Answered by ajfour last updated on 25/Jan/18 $$Ifnewcoordinateaxesbe$$$$tangentatA\left(towardsright\right)$$$$xaxisandaxisofparabolathe$$$$yaxis\left(upwards\right),theneq.of$$$${parabola}\:{is}\:\:\boldsymbol{{y}}=\boldsymbol{{px}}^{\mathrm{2}}…

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