if x2 + y2 -2x + 2ay +a + 3 =0 represents a real circle with non zero radius - Maths - Conic Sections

Question

if x2 + y2 -2x + 2ay +a + 3 =0 represents a real circle with non
zero radius then a belongs to

a) (-inifinty , -1)
b) (-1,2)
c)(2,infinty)
d)(-infinity, -1)union (2,infinty)

Vivek Rai · Accepted Answer

Dear student
The circle is x2+y2-2x+2ay+a+3=0The center of circle=-(coefficient of x)2,-(coefficient of y)2=1,-aradius= (x coordinate of center)2+(y coordinate of circle)2-c=1+a2-a-3, for this to represent a real circle with non zero radius , we have, a2-a-2>0⇒(a+1)(a-2)>0 ⇒a∈(-∞,-1)∪(2,∞)
Hope this clears your doubt
With regards

if x2 + y2 -2x + 2ay +a + 3 =0 represents a real circle with non zero radius then a belongs to a) (-inifinty , -1) b) (-1,2) c)(2,infinty) d)(-infinity, -1)union (2,infinty)

if x2 + y2 -2x + 2ay +a + 3 =0 represents a real circle with non zero radius then a belongs to

a) (-inifinty , -1)
b) (-1,2)
c)(2,infinty)
d)(-infinity, -1)union (2,infinty)