⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━{\large{\BOLD{\rm{\large{Given \; that}}}}}Giventhat★ The axis is along x-axis and PASSING through the point (2, 3).{\large{\bold{\rm{\large{To \; DETERMINE}}}}}Todetermine★ The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is ?{\large{\bold{\rm{\large{Solution}}}}}Solution★ The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is {\bold{\red{2y^{2} \: = \: 9x}}}2y 2 =9x⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━{\large{\bold{\rm{\large{Using \: concept}}}}}Usingconcept★ The equation of parabola with vertex at origin the axis is given by what?{\large{\bold{\rm{\large{Using \: formula}}}}}Usingformula★ The equation of parabola with vertex at origin the axis is given by {\bold{\red{y^{2} \: = \: 4ax}}}y 2 =4ax{\tt{Here,}}Here,\; \; \; \; \; \;{\bold{\longrightarrow y^{2} \: is \: 3^{2}}}⟶y 2 is3 2 \; \; \; \; \; \;{\bold{\longrightarrow x \: is \: 2}}⟶xis2⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━{\large{\bold{\rm{\large{Full \; Solution}}}}}FullSolution~ Now we have to PUT the values according to the dimension..!{\sf{:\implies y^{2} \: = 4ax}}:⟹y 2 =4ax{\sf{:\implies 3^{2} \: = 4a(2)}}:⟹3 2 =4a(2){\sf{:\implies 3 \TIMES 3 \: = 4a(2)}}:⟹3×3=4a(2){\sf{:\implies 9 \: = 4a(2)}}:⟹9=4a(2){\sf{:\implies 9 \: = 8a}}:⟹9=8a{\sf{:\implies 9/8 \: = a}}:⟹9/8=a{\sf{:\implies a \: = 9/8}}:⟹a=9/8~ Now let's us imply the value of a as 9/8 in that dimension again to get correct and full solution..!{\sf{:\implies y^{2} \: = 4ax}}:⟹y 2 =4ax{\sf{:\implies y^{2} \: = 4(9/8)x}}:⟹y 2 =4(9/8)x{\sf{:\implies y^{2} \: = (9/2)x}}:⟹y 2 =(9/2)x(× = ÷) ; (÷ = ×){\sf{:\implies 2y^{2} \: = 9x}}:⟹2y 2 =9x⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━Explanation:⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━{\large{\bold{\rm{\large{Given \; that}}}}}Giventhat★ The axis is along x-axis and passing through the point (2, 3).{\large{\bold{\rm{\large{To \; determine}}}}}Todetermine★ The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is ?{\large{\bold{\rm{\large{Solution}}}}}Solution★ The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is {\bold{\red{2y^{2} \: = \: 9x}}}2y 2 =9x⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━{\large{\bold{\rm{\large{Using \: concept}}}}}Usingconcept★ The equation of parabola with vertex at origin the axis is given by what?{\large{\bold{\rm{\large{Using \: formula}}}}}Usingformula★ The equation of parabola with vertex at origin the axis is given by {\bold{\red{y^{2} \: = \: 4ax}}}y 2 =4ax{\tt{Here,}}Here,\; \; \; \; \; \;{\bold{\longrightarrow y^{2} \: is \: 3^{2}}}⟶y 2 is3 2 \; \; \; \; \; \;{\bold{\longrightarrow x \: is \: 2}}⟶xis2⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━{\large{\bold{\rm{\large{Full \; Solution}}}}}FullSolution~ Now we have to put the values according to the dimension..!{\sf{:\implies y^{2} \: = 4ax}}:⟹y 2 =4ax{\sf{:\implies 3^{2} \: = 4a(2)}}:⟹3 2 =4a(2){\sf{:\implies 3 \times 3 \: = 4a(2)}}:⟹3×3=4a(2){\sf{:\implies 9 \: = 4a(2)}}:⟹9=4a(2){\sf{:\implies 9 \: = 8a}}:⟹9=8a{\sf{:\implies 9/8 \: = a}}:⟹9/8=a{\sf{:\implies a \: = 9/8}}:⟹a=9/8~ Now let's us imply the value of a as 9/8 in that dimension again to get correct and full solution..!{\sf{:\implies y^{2} \: = 4ax}}:⟹y 2 =4ax{\sf{:\implies y^{2} \: = 4(9/8)x}}:⟹y 2 =4(9/8)x{\sf{:\implies y^{2} \: = (9/2)x}}:⟹y 2 =(9/2)x(× = ÷) ; (÷ = ×){\sf{:\implies 2y^{2} \: = 9x}}:⟹2y 2 =9x⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━