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| PAGE: 40 | SET: Exercises | PROBLEM: 59 |
Observe the graph :
The center of circle in the graph is located at first quadrant and passes through origin.
Standard form of circle equation is 
, where 
is center and 
is radius.
Determine which of the below equations are centered at first quadrant and passes through the origin.
Write the each equation in standard form.
Check the sign of coordinates of center of each circle.
Check the equations which are satisfy at 
.
(a). The circle equation is 
.
Compare it with standard form of circle equation is 
The 
-coordinate of center of the circle is negative.
Substitute in above equation.
The above circle passes through origin.
(b). The circle equation is 
.
The coordinates of center of circle are positive.
Substitute in above equation.
The above circle passes through origin.
(c). The circle equation is 
.
The coordinates of center of circle are positive.
Substitute in above equation.
The above circle passes through origin.
(d). The circle equation is 
.
The 
-coordinate of center of the circle is negative.
Substitute 
in above equation.
The above circle passes through origin.
By using completing square method convert the below equations in to standard form of circle.
(e). The circle equation is 
.
To change expression in to a perfect square trinomials add 
and 
to each side of expressions.
The coordinates of center of circle are positive.
Substitute in above equation.
The above circle passes through origin.
(f). The circle equation is 
.
The 
-coordinate of center of circle is negative.
Substitute in above equation.
The above circle passes through origin.
(g). The circle equation is 
.
The coordinates of center of circle are positive.
Substitute in above equation.
The above circle passes through origin.
(h). The circle equation is 
.
The coordinates of center of circle is positive.
Substitute in above equation.
The above circle does not passes through origin.
Possible equations are (b), (c), (e), (g).
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