Question Number 76013 by vishalbhardwaj last updated on 22/Dec/19
Answered by som(math1967) last updated on 22/Dec/19
$$\left({y}−\mathrm{4}\right)^{\mathrm{2}} =\mathrm{4}.\mathrm{3}\left({x}−\mathrm{9}\right) \\ $$$$\therefore{Vertex}\:\left(\mathrm{9},\mathrm{4}\right)\:\:{focus}\left(\mathrm{3}+\mathrm{9}\:,\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\mathrm{12},\mathrm{4}\right) \\ $$$${equation}\:{of}\:{directrix}\:{x}+\mathrm{3}=\mathrm{9} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}−\mathrm{6}=\mathrm{0} \\ $$$${Latus}\:{rectum}\:\mathrm{4}.\mathrm{3}=\mathrm{12}{unit} \\ $$
Commented by vishalbhardwaj last updated on 22/Dec/19
$$\mathrm{please}\:\mathrm{explain}\:\mathrm{with}\:\mathrm{complete}\:\mathrm{steps} \\ $$
Commented by som(math1967) last updated on 22/Dec/19
![(y−4)^2 =12(x−9) is comparable Y^2 =4aX here Y=y−4, X=(x−9) for Y^2 =4aX vertex X=0 ∴x−9=0⇒x=9 Y=0 ⇒y−4=0 ⇒y=4 focus X=a ⇒X=3 [4a=12 ⇒a=3] x−9=3 ⇒x=12 Y=0 (y−4)=0 y=4 eqn. directrix X=−a x−9=−3⇒ x−6=0](https://www.tinkutara.com/question/Q76025.png)
$$\left({y}−\mathrm{4}\right)^{\mathrm{2}} =\mathrm{12}\left({x}−\mathrm{9}\right)\:{is}\:{comparable} \\ $$$${Y}^{\mathrm{2}} =\mathrm{4}{aX} \\ $$$${here}\:{Y}={y}−\mathrm{4},\:{X}=\left({x}−\mathrm{9}\right) \\ $$$$\:{for}\:{Y}^{\mathrm{2}} =\mathrm{4}{aX}\: \\ $$$$\:{vertex}\:{X}=\mathrm{0}\:\therefore{x}−\mathrm{9}=\mathrm{0}\Rightarrow{x}=\mathrm{9} \\ $$$$\:\:{Y}=\mathrm{0}\:\Rightarrow{y}−\mathrm{4}=\mathrm{0}\:\Rightarrow{y}=\mathrm{4} \\ $$$${focus}\:\:{X}={a}\:\:\Rightarrow{X}=\mathrm{3}\:\:\:\:\left[\mathrm{4}{a}=\mathrm{12}\:\Rightarrow{a}=\mathrm{3}\right] \\ $$$$\:\:{x}−\mathrm{9}=\mathrm{3}\:\Rightarrow{x}=\mathrm{12}\:\:{Y}=\mathrm{0}\:\left({y}−\mathrm{4}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}=\mathrm{4} \\ $$$${eqn}.\:{directrix}\:\:{X}=−{a} \\ $$$$\:\:\:\:\:\:{x}−\mathrm{9}=−\mathrm{3}\Rightarrow\:{x}−\mathrm{6}=\mathrm{0} \\ $$
Commented by vishalbhardwaj last updated on 22/Dec/19
$$\mathrm{thanks}\:\mathrm{a}\:\mathrm{lot} \\ $$