Let p and q be non – zero real numbers. Then the equation

$\left(p{x}^2+q{y}^2+r\right)\left(4x^2+4y^2-8x-4\right)=0$ represent(s)

$\left(p{x}^2+q{y}^2+r\right)\left(4x^2+4y^2-8x-4\right)=0$

$\Rightarrow 4x^2+4y^2-8x-4=0$

$\Rightarrow {\left(x-1\right)}^2+y^2=2$

$orp{x}^2+q{y}^2+r=0$  will represents 

(i) two straight lines if r = 0 and p, q are of opposite sign

(ii) a circle if p = q and ‘r’ is of opposite sign that of p.

(iii) a hyperbola if p and q are opposite sign and $r\ne 0$

(iv) and ellipse if p and q are unequal but of same sign and ‘r’ is of sign opposite to that of  ‘p’.