Question

Obtain the parametric equation of the circle represented by
x? + y2 +6x+8y-96=0
x=-3+11coso
y=-4+11sin e
x=3+11cose
y=4+11sino
x=11cose
y =11sino
x = 6 cos o
y=6sin e​

Answer 1

Given,

equation of circle is represented by, x² + y² + 6x + 8y - 96 = 0.

To find,

Parametric equation of given circle.

we know, if x² + y² + 2gx + 2fy + c = 0 is equation of circle when centre is (-g, -f) and radius, r = √(g² + f² - c).

then parametric equation of circle is ...

x = -g + rcosθ , y = -f + rsinθ

where θ is angle made by line drawn from centre of circle to origin with x-axis.

here equation of circle is x² + y² + 6x + 8y - 96 = 0

so centre = (-3, -4)

radius , r = √(3² + 4² - 96) = √(25 + 96) = √121 = 11

now parametric equation of circle, x = -3 + 11cosθ and y = -4 + 11sinθ