Notes

 

Problems

\(\textbf{1)}\) Express in Cartesian Standard Form.
\( x=1+3 \cos⁡{t} \)
\( y=2+5 \sin⁡{t} \)

Show Answer

The answer is Ellipse \( \frac{(x-1)^2}{9}+\frac{(y-2)^2}{25}=1 \)

 

\(\textbf{2)}\) Express in Cartesian Standard Form.
\( x=-3+4 \cos⁡{t} \)
\( y=-1+4 \sin⁡{t} \)

Show Answer

The answer is Circle \( (x+3)^2+(y+1)^2=16 \)

 

\(\textbf{3)}\) Express in Cartesian Standard Form.
\( x=6+5 \cos⁡{t} \)
\( y=-2+\sin⁡{t} \)

Show Answer

The answer is Ellipse \( \frac{(x-6)^2}{25}+\frac{(y+2)^2}{1}=1 \)

 

\(\textbf{4)}\) Express in Cartesian Standard Form.
\( x=3 \cos⁡{t} \)
\( y=2+3 \sin⁡{t} \)

Show Answer

The answer is Circle \( x^2+(y-2)^2=9 \)

 

\(\textbf{5)}\) Express in Cartesian Standard Form.
\( x=1+3 \tan⁡{t} \)
\( y=2+5 \sec⁡{t} \)

Show Answer

The answer is Hyperbola \( -\frac{(x-1)^2}{9}+\frac{(y-2)^2}{25}=1 \)

 

\(\textbf{6)}\) Express in Cartesian Standard Form.
\( x=1+3 \sec⁡{t} \)
\( y=2+5 \tan⁡{t} \)

Show Answer

The answer is Hyperbola \( \frac{(x-1)^2}{9}-\frac{(y-2)^2}{25}=1 \)

 

See Related Pages\(\)

\(\bullet\text{ All Conic Section Notes}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Equation of a Circle}\)
\(\,\,\,\,\,\,\,\,(x-h)^2+(y-k)^2=r^2…\)

\(\bullet\text{ Parabolas}\)
\(\,\,\,\,\,\,\,\,y=a(x-h)^2+k…\)

\(\bullet\text{ Axis of Symmetry}\)
\(\,\,\,\,\,\,\,\,x=-\frac{b}{2a}…\)

\(\bullet\text{ Ellipses}\)
\(\,\,\,\,\,\,\,\,\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1…\)

\(\bullet\text{ Area of Ellipses}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\pi a b…\)

\(\bullet\text{ Hyperbolas}\)
\(\,\,\,\,\,\,\,\,\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1…\)

\(\bullet\text{ Conic Sections- Completing the Square}\)
\(\,\,\,\,\,\,\,\,x^2+8x+y^2−6y=11 \Rightarrow (x+4)^2+(y−3)^2=36…\)

\(\bullet\text{ Conic Sections- Parametric Equations}\)
\(\,\,\,\,\,\,\,\,x=h+r \cos{t}\)
\(\,\,\,\,\,\,\,\,y=k+r \sin{t}…\)

\(\bullet\text{ Degenerate Conics}\)
\(\,\,\,\,\,\,\,\,x^2−y^2=0…\)