For Exercise 41-54, write the equation in the form x − h 2 + y − k 2 = c . Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x 2 + y 2 + 22 x − 4 = 0
For Exercise 41-54, write the equation in the form x − h 2 + y − k 2 = c . Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x 2 + y 2 + 22 x − 4 = 0
Solution Summary: The author explains the standard form of the equation x2+y2,+22x-4=0. The equation represents a circle with center and radius.
For Exercise 41-54, write the equation in the form
x
−
h
2
+
y
−
k
2
=
c
.
Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4)
Recall that an equation of a circle can be written in standard form (x-h)² + (y-k)² = r, where (h, k) is the
center and r is the radius.
After expanding both squares, moving all terms to the left-hand side, and combining like terms, the equation
can also be written in the form x² + y² + Ax+By+ C = 0, where A, B, and C are constants.
a. Find an equation of the form x2 + y² + Ax+By+C =0 for the circle that passes through the points
(6, 0), (2, 2), and (7,-3).
To do so, find the values of A, B, and C by writing and solving a system of 3 linear equations.
System:
Show the steps of solving the system.
Equation in Standard Form:
Solution:
b. Rewrite the equation found in part (a) in standard form using the technique of completing the square.
c. Use your result in part (b) to determine the center and radius of the circle.
Center:
A =
B =
C =
Radius:
can you solve g, h, and j too please?
Prove the equations
= 1 and x = x+2 are
x-2
equivalent?. Explain why or why not.
Elementary Statistics: Picturing the World (7th Edition)
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