For the parametric equations: \(x = t + 1\) , \(y = {t^2} - 1\) the cartesian equation is?
\(y = {x^2} - 2x\)
For the parametric equations : \(x = 9\sin \theta \) , \(y = 9\cos \theta \) the cartesian equation is?
\({x^2} + {y^2} = 81\)
For the cartesian equation \({x^2} = 4(y - 2)\) the parametric equations are?
\(x = 2t\,\,\,\,y = {t^2} + 2\)
For the cartesian equation \({(x - 1)^2} + {(y + 1)^2} = 4\) the parametric equations are?
\(x = 1 + 2\sin \theta ,\,\,y = - 1 + 2\cos \theta \)
For the parametric equations: \(x = 2t - 1\), \(y = 1 + t\) the cartesian equation is?
\(x - 2y + 3 = 0\)
Change the parametric form of the line \(x = 2t\), \(y = 4 + 3t\) into the Cartesian form.
\(3x - 2y + 8 = 0\)
Change the cartesian form of the line \(2x + 3y - 6 = 0\) into the parametric form.
\(x = 3t,\,\,y = 2 - 2t\)
Change the parametric form of the circle \(x = 2 + \sin \theta \), \(y = 1 + \cos \theta \) into the cartesian form.
\({(x - 2)^2} + {(y - 1)^2} = 1\)
Change the Cartesian form of the circle \({(x - 3)^2} + {(y + 2)^2} = 4\) into the parametric form.
\(x = 3 + 2\sin \theta ,\,y = - 2 + 2\cos \theta \)
Change the cartesian form of the circle \(x^2+y^2+2 x-6 y=0\) into the parametric form.
\(x=-1+\sqrt{10} \cos \theta, y=3+\sqrt{10} \sin \theta\)
Change the cartesian form of the parabola \(y=\dfrac{1}{4} x^2-2 x+1\) into the parametric form.
\(x=2 t+4, y=t^2-3\)
(i) Change the parametric form of the circle \(x=-3+4 \cos \theta, y=2+4 \sin \theta\) into the cartesian form.
(ii) Sketch this circle in the domain \(-7 \leq x \leq 1\).
i) \((x+3)^2+(y-2)^2=16\)
ii) Refer to worked solution
Change the cartesian form of the circle \(x^2+y^2+6 x-4 y=3\) into the parametric form.
\(x=-3+4 \cos \theta, y=2+4 \sin \theta\)
(i) Change the parametric form of the straight line \(x=3 t-1, y=2 t+1\) into the cartesian form.
(ii) Sketch this straight line in the domain \(-3 \leq x \leq 3\).
i) \(2 x-3 y+5 =0\)
Change the cartesian form of the line \( y=\dfrac{3}{5}{x-4}\) into the parametric form.
\(x=5 t, y=-4+3 t\)
(i) Change the parametric form of the parabola \(x=2-p, y=3-p^2\) into the cartesian form.
(ii) Sketch this parabola in the domain \(-1 \leq x \leq 5\).
i) \(y=3-(x-2)^2\)
Change the parametric form of the parabola \(x=2 a p, y=a p^2\) into the cartesian form.
\(x^2=4 a y\)
Change the cartesian form of the parabola \((x-1)^2=4(y+2)\) into the parametric form.
\(x=2 t+1, y=t^2-2\)
(i) Change the parametric form of the straight line \(x=1-t, y=4 t\) into the cartesian form.
(ii) Sketch this straight line in the domain \(-1 \leq x \leq 2\).
\(4 x+y-4=0\)
Change the cartesian form of the line \(3 x-2 y-12=0\) into the parametric form.
\(x=2 t, y=-6+3 t\)
(i) Change the parametric form of the parabola \(x=2 p+1, y=1-p^2\) into the cartesian form.
(ii) Sketch this parabola in the domain \(-2 \leq x \leq 4\).
i) \(y =-\dfrac{1}{4}(x-1)^2+1\)
Change the cartesian form of the parabola \((y+2)^2=8(x-1)\) into the parametric form.
\(x=2 t^2+1, y=4 t-2\)
(i) Change the parametric form of the circle \(x=2+2 \cos \theta, y=-1+2 \sin \theta\) into the cartesian form.
(ii) Sketch this circle in the domain \(-1 \leq x \leq 5\).
i) \((x-2)^2+(y+1)^2=4\)
Change the cartesian form of the circle \(x^2+y^2+4 x+2 y=20\) into the parametric form.
\(x=-2+5 \cos \theta, y=-1+5 \sin \theta\)
(i) Change the parametric form of the straight line \(x=1-t, y=1+t\) into the cartesian form.
(ii) Sketch this straight line in the domain \(-2 \leq x \leq 2\).
i) \(x+y-2=0\)
Change the cartesian form of the line \(\dfrac{x}{2}+\dfrac{y}{3}=1\) into the parametric form.
\(x=2 t, y=3-3 t\)
(i) Change the parametric form of the parabola \(x=p+1, y=p^2-1\) into the cartesian form.
(ii) Sketch this parabola in the domain \(-1 \leq x \leq 3\).
i) \(y=(x-1)^2-1\)
Change the cartesian form of the parabola \(y=x^2+2 x-3\) into the parametric form.
\(x=\dfrac{t}{2}-1, y=\dfrac{1}{4} t^2-4\)
(i) Change the parametric form of the circle \(x=3+3 \cos \theta, y=3+3 \sin \theta\) into the cartesian form.
(ii) Sketch this circle in the domain \(-1 \leq x \leq 7\).
i) \((x-3)^2+(y-3)^2=9\)
