How many times does the line y=-6 intersect with the circle x^2+y^2=36?
1 answer:
Answer:
a) The line intersects with the circle once.
b) Tangent
Step-by-step explanation:
We are given the following equation for the circle:
How many times does the line y=-6 intersect with the circle?
We have to find the values of x when
So
Since the line intersects the circle at one point, it is tangent to the circle.
The line intersects with the circle once.
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Let us denote the smaller even integer by 
.
Then, the next even integer must be
.
To verify, set as any even number, say 
.
Then, the next even integer must be 2 more than this number, i.e.
.
The sum of these two consecutive even integers can be expressed as:
We are told that this sum divided by four is 189.5, i.e.
Multiplying both sides by 4 will reverse the division:
Subtracting 2 from each side will reverse the addition:
Dividing both sides by 2 will reverse the multiplication:
Therefore, the two consecutive integers must be 378 and 380.
Check this:
Then, the next even integer must be
To verify, set
Then, the next even integer must be 2 more than this number, i.e.
The sum of these two consecutive even integers can be expressed as:
We are told that this sum divided by four is 189.5, i.e.
Multiplying both sides by 4 will reverse the division:
Subtracting 2 from each side will reverse the addition:
Dividing both sides by 2 will reverse the multiplication:
Therefore, the two consecutive integers must be 378 and 380.
Check this:
Look for what 'y' is when t = 1 and t = 2. Go to the graph, look at 1 on the bottom axis and go up till you find the point, then go all the way to the left to see what the y-value is, in this case it should be 1200. If you do the same with t = 2, you will get 2400. So our two ordered pairs are:
(1, 1200), (2, 2400)
We can find the slope of these two points by plugging them into the slope formula:
For points in the form of (x1, y1), (x2, y2). Plug in what we know:
Subtract:
Divide:
This is the slope, so we can write the equation:
(1, 1200), (2, 2400)
We can find the slope of these two points by plugging them into the slope formula:
For points in the form of (x1, y1), (x2, y2). Plug in what we know:
Subtract:
Divide:
This is the slope, so we can write the equation:
Domain is the x-coordinate and range is the y - coordinate