3,000 Solved Problems in Calculus 26 - CHAPTER 4 Circles...

CHAPTER 4
Circles
4.1 Write the standard equation for a circle with center at (a, b) and radius r.
y the distance formula, a point (x, y) is on the circle if and only if
both sides, we obtain the standard equation: (x — a)
2
+ (y — b)
2
= r
2
.
4.2 Write the standard equation for the circle with center (3,5) and radius 4.
4.3 Write the standard equation for the circle with center (4, -2) and radius 7.
4.4 Write the standard equation for the circle with center at the origin and radius r.
4.5 Find the standard equation of the circle with center at (1, -2) and passing through the point (7, 4).
Complete the square in x and in y: (x - 6)
2
+ (y + 10)
2
+ 15 = 36 + 100. [Here the-6 in (x - 6) is half
of the coefficient, -12, of x in the original equation, and the + 10in (_y + 10) is half of the coefficient 20, of y.
The 36 and 100 on the right balance the squares of -6 and +10 that have in effect been added on the left.]
Simplifying, we