Answer:
See below for graphs
- (2, -3), r = 2 (blue)
- (-3, -1), r = 1 (green)
- (3, -1), r = 3 (purple)
- (4, 1), r = 3 (red)
Step-by-step explanation:
I like to solve a set of problems like this once, then use a calculator or spreadsheet to crunch the numbers.
We can start with the general form of the equation for a circle:
x^2 +y^2 +ax +by +c = 0
Completing the square gives ...
(x^2 +ax +(a/2)^2) +(y^2 +by +(b/2)^2) = (a/2)^2 +(b/2)^2 -c
(x +(a/2))^2 +(y +(b/2))^2 = (a/2)^2 +(b/2)^2 -c
Comparing this to the standard form formula ...
(x -h)^2 + (y -k)^2 = r^2
we see the relations are ...
- h = -a/2
- k = -b/2
- r = √((a/2)² +(b/2)² -c)
where (h, k) is the center and r is the radius.
Then your circle centers and radii are ...
- (h, k) = (-(-4)/2, -6/2) = (2, -3); r = √(4+9-9) = 2
- (h, k) = (-6/2, -2/2) = (-3, -1); r = √(9+1-9) = 1
- (h, k) = (-(-6)/2, -2/2) = (3, -1); r = √(9+1-1) = 3
- (h, k) = (-(-8)/2, -(-2)/2) = (4, 1); r = √(16+1-8) = 3
A tangent (here WZ in the question) to any circle (here O in the question) is a line segment that touches the circle at only one point (here B in the question) on circumference of circle, and the radius of the circle (here OB in the question) through this point is always perpendicular to that particular tangent.
In other words, Tangent (WZ) and Radius (OB) of any circle (O) always make a Right angle at point of intersection (B) on its circumference.
It means angle ∠OBZ would be a Right angle i.e. 90 degrees.
So, option B i.e. 90 degrees is the final answer.
Answer:
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Here is answer in the picture I hope this will help to you
Answer:
<em>4 is the unit's digit of the 20th number.</em>
Step-by-step explanation:
Let us try to find out a pattern for the unit's digit of the terms.
1st term is 1, so unit's digit of 1st term is 1.
2nd term 
so unit's digit is 4.
3rd term 
so unit's digit is 9.
4th term 
so unit's digit is 4.
5th term's unit digit: Square of unit's digit of 4th term + 3
i.e. 9.
:
We can see that the pattern is
3rd, 5th, 7th ...... terms have 9 as the unit's digit.
2nd, 4th, 6th.... terms have 4 as the unit's digit.
So, 20th term will have 4 as the unit's digit.
