Which one of the following equation represent parametric equation to a parabolic curve? `x=3cost ; y=4sint` `x^2-2=2cost ; y=4cos^2t/2` `sqrt(x)=tant

Question

Which one of the following equation represent parametric equation to a parabolic curve? `x=3cost ; y=4sint` `x^2-2=2cost ; y=4cos^2t/2` `sqrt(x)=tant

Which one of the following equation represent parametric equation to a parabolic curve? `x=3cost ; y=4sint` `x^2-2=2cost ; y=4cos^2t/2` `sqrt(x)=tant ;sqrt(y)=sect` `x=sqrt(1-sint ;)y=sint/2+cost/2`
A. `x=3cost,y=4sint`
B. `x^(2)-2=2cost,y=4"cos"^(2)(t)/(2)`
C. `sqrt(x)=tant,sqrt(y)=sect`
D. `x=sqrt(1-sint),y="sin"(t)/(2)+"cos"(t)/(2)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - B
(2) `x=3cost,y=4sint`
Eliminating t, we have
`(x^(2))/(9)+(y^(2))/(16)=1`
which is an ellipse.
`x^(2)-2=2cost andy=4"cos"^(2)(t)/(2)`
`or" "y=2(1+cost)`
`and" "y=2(1+(x^(2)-2)/(2))`
which is a parabola.
`sqrt(x)=tant,sqrt(y)=sect`
Eliminating t, we have
y-x=1
which is a straight line.
`x=sqrt(1-sint)`
`y="sin"(t)/(2)+"cos"(t)/(2)`
Eliminating t, we have `x^(2)+y^(2)=1-sint+1+sint=2`
which is a circle.