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Which one of the following equation represent parametric equation to aparabolic 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)` |
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Answer» 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. |
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