Maharashtra BoardEnglish MediumSTD 11 ScienceMathsCircle2 Marks
Question
Write the parametric equations of the circles:
$x^2+y^2+2 x-4 y-4=0$
✓
Answer
Given equation of the circle is
$x^2+y^2+2 x-4 y-4=0$
$\Rightarrow x^2+2 x+y^2-4 y-4=0$
$\Rightarrow x^2+2 x+1-1+y^2-4 y+4-4-4=0$
$\Rightarrow\left(x^2+2 x+1\right)+\left(y^2-4 y+4\right)-9=0$
$\Rightarrow(x+1)^2+(y-2)^2=9$
$\Rightarrow(x+1)^2+(y-2)^2=3^2$
Comparing this equation with $(x-h)^2+(y-k)^2=r^2$, we get
h = -1, k = 2 and r = 3
The parametric equations of the circle in terms of θ are
x = h + r cos θ and y = k + r sin θ
⇒ x = -1 + 3 cos θ and y = 2 + 3 sin θ
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