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Answers
Answer:
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{\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
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{\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
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{\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
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