# How do you transform parametric equations into Cartesian form: x= 3 + 2 cost and y= 1 + 5sint?

Aug 7, 2016

$25 {x}^{2} + 4 {y}^{2} - 150 x - 8 y + 129 = 0$

#### Explanation:

As $x = 3 + 2 \cos t$ and $y = 1 + 5 \sin t$,

we have $\cos t = \frac{x - 3}{2}$ and $\sin t = \frac{y - 1}{5}$

Hence ${\left(\frac{x - 3}{2}\right)}^{2} + {\left(\frac{y - 1}{5}\right)}^{2} = 1$ or

$\frac{{x}^{2} - 6 x + 9}{4} + \frac{{y}^{2} - 2 y + 1}{25} = 1$ or

$25 \left({x}^{2} - 6 x + 9\right) + 4 \left({y}^{2} - 2 y + 1\right) = 100$ or

$25 {x}^{2} + 4 {y}^{2} - 150 x - 8 y + 225 + 4 - 100 = 0$ or

$25 {x}^{2} + 4 {y}^{2} - 150 x - 8 y + 129 = 0$

graph{25x^2+4y^2-150x-8y+129=0 [-7.295, 12.705, -3.92, 6.08]}