tmua 2022 Q4

tmua · Uk · paper2 1 marks Circles Distance from Center to Line
The point $P$ has coordinates $( p , q )$, and the equation of a circle is
$$x ^ { 2 } + 2 f x + y ^ { 2 } + 2 g y + h = 0$$
where $f , g , h , p$ and $q$ are all real constants. Let $L$ be the distance between the centre of the circle and the point $P$. Which one of the following is sufficient on its own to be able to calculate $L$ ?
A the values of $f , g$ and $h$
B the values of $f , g , p$ and $q$
C the values of $f , h , p$ and $q$
D the values of $g , h , p$ and $q$
E none of the options A-D is sufficient on its own
..... 6
The point $P$ has coordinates $( p , q )$, and the equation of a circle is

$$x ^ { 2 } + 2 f x + y ^ { 2 } + 2 g y + h = 0$$

where $f , g , h , p$ and $q$ are all real constants.\\
Let $L$ be the distance between the centre of the circle and the point $P$.\\
Which one of the following is sufficient on its own to be able to calculate $L$ ?\\
A the values of $f , g$ and $h$\\
B the values of $f , g , p$ and $q$\\
C the values of $f , h , p$ and $q$\\
D the values of $g , h , p$ and $q$\\
E none of the options A-D is sufficient on its own