Question

find the parameteric equation for the given curve (x-1)^2+(y+2)^2=9
​

Answer 1

Answer:

the most sensible/common paramaterisation here is to recognise that this is a circle, or just to acknowledge the Pythagorean identity: #cos^2 t + sin^2 t = 1#, that we could use here

so if we take your equation

#x^2+y^2=16#

...and re-write it slightly as

#(x/4)^2+(y/4)^2=1#

then we see that if we set

#x/4 = cos t# and #y/4= sin t#

we can use the identity

So the parameterisation is

#((x), (y)) = ((4 cos t),(4 sin t))#

so that, just to check, #x^2+y^2= 4^2 cos^2 t + 4^2 sin^2 t = 16#

Step-by-step explanation:

please mark as brainliest

Answer 2

Answer:

An example

Step-by-step explanation:

4(x  2 +y  2 )=9

Divide the equation by 4

x  2  +y  2 =  4 9

​Here, r  2 =  4 9

​ ⟹r=  2 3

​ The parametric equations of the circle x  

2 +y  

2  =r  2

 in parameter θ are x=rcosθ, y=rsinθ

The parametric equations of the given circle is,

x= 2 3

​  cosθ, y=  2 3

​ sinθ and 0≤θ≤2π