Find the center of a circle with the equation: x2+y2−4x+2y−11=0
2 answers:
The standard form for the equation of a circle is
The center of such a circle is the point with coordinates (h, k).
To get your equation into that form, you have to complete the square (twice; once for x and once for y).
Add 11 to both sides so the constant appears on the right. Build in some space to add a couple of numbers, like this:
To complete the square on x, look at the coefficient of x (that's -4), take half of it (that's -2), then square it (that's 4). Add 4 inside the first pair of (). Do the same kind of thing for y -- half of 2 is 1 and 1 squared is 1; add 1 inside the second pair of (). Be sure to add 4 and 1 to the right side, too.
The first three terms factor and the next 3 terms factor.
Match this up with the standard form
The center of the circle is (2, -1).
The center of such a circle is the point with coordinates (h, k).
To get your equation into that form, you have to complete the square (twice; once for x and once for y).
Add 11 to both sides so the constant appears on the right. Build in some space to add a couple of numbers, like this:
To complete the square on x, look at the coefficient of x (that's -4), take half of it (that's -2), then square it (that's 4). Add 4 inside the first pair of (). Do the same kind of thing for y -- half of 2 is 1 and 1 squared is 1; add 1 inside the second pair of (). Be sure to add 4 and 1 to the right side, too.
The first three terms factor and the next 3 terms factor.
Match this up with the standard form
The center of the circle is (2, -1).
You might be interested in
Answer:
Step-by-step explanation:
We are asked to find x, a missing side in a triangle.
This is a right triangle because there is a small square in the corner representing a 90 degree or right angle. Therefore, we can use right triangle trigonometry. The three main functions are:
- sinθ= opposite/hypotenuse
- cosθ= adjacent/hypotenuse
- tanθ= opposite/adjacent
Examine the triangle. We will use angle S, measuring 54 degrees, for theta. Side QR, measuring x, is <u>opposite</u> angle S. Side QS, measuring 2.3, is the <u>hypotenuse</u> because it is opposite the right angle. Since we have the opposite and hypotenuse, we will use sine.
- θ= 54
- opposite= x
- hypotenuse = 2.3
We are solving for x, so we must isolate the variable. It is being divided by 2.3 The inverse operation of division is multiplication, so we multiply both sides by 2.3
Round to the nearest tenth. The 6 in the hundredth place to the right tells us to round the 8 up to a 9.
x is approximately <u>1.9</u>
Answer:
None of those options
Step-by-step explanation:
I just did the work myself and even ran it through a calculator but the correct answer isn't one of those options. Here's my work:
I'd contact you teacher about that...it might be an error in their system (it's happened to me a few times before where the correct answer is marked as incorrect or isn't even an option)