Question

The parametric equations of the circle
x2 + y2 + 2x + 4y - 11 = 0 are​

Answer 1

Answer:

I hope it will help you..............

Answer 2

The equations are x= -1+4cosθ and y= -2+4sinθ.

Given:

x2 + y2 + 2x + 4y - 11 = 0

To find:

The parametric equations of the circle

Solution:

We will complete the given equation and obtain the coordinates of the circle's centre.

The given equation-

$x^{2}$ + $y^{2}$+ 2x + 4y - 11 = 0

$x^{2}$ + $y^{2}$+2x+4y=11

Adding 1 and 4 on both sides of the equation,

$x^{2}$ + $y^{2}$+2x+4y+1+4=11+1+4

$x^{2}$+2x+1+ $y^{2}$+4y+4=16

$(x+1)^{2}$+$(y+2)^{2}$=16

$(x+1)^{2}$+$(y+2)^{2}$= $4^{2}$

So, the coordinates of the circle's centre, (h, k)=(-1, -2) and the radius, r=4 units.

Now, the parametric equations are as follows-

x= h+r cosθ

y= k+r sinθ

Using values,

x= (-1)+4cosθ

x= -1+4cosθ

y= (-2)+4sinθ

y= -2+4sinθ

Therefore, the equations are x= -1+4cosθ and y= -2+4sinθ.

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