CUET PG 2024 — Mathematics PYQ

A general second--degree equation of a conic is  
$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$,  
where $a,b,c,f,g,$ and $h$ are constants.

Which of the following statements are true?

(A) The given conic is a circle if $a=0$ and $b=0$

(B) The given conic is a circle if $a=b\ne 0$ and $h=0$

(C) The given conic is a circle if $a=b\ne 0$ and $h\ne 0$

(D) The given conic represents a pair of real and distinct straight lines if  
$f=g=c=0$ and h^{2} - ab > 0

Choose the correct answer from the options given below.