First of all we have to figure out what type of a conic this is. We know it's not a parabola because it has both an x-squared term and a y-squared term. There's a plus sign separating the squared terms so we know it also cannot be a hyperbola. It's either a circle or an ellipse. If this was simply a circle, though, we would not have leading coefficients on the squared terms (other than a 1). Circles have a standard form of 
. That makes this an ellipse. Let's group together the x terms and the y terms and move the constant over and complete the squares to see what we have. 
. Since there's only 1 term with the x squared expression we cannot complete the square on the x's but we can on the y terms. First, though, the rule for completing the square is that the leading coefficient has to be a 1 and ours is a 25, so let's factor it out. 
. To complete the square we take half the linear term, square it, and add it to both sides. Our linear term is 8. Half of 8 is 4, and 4 squared is 16. So we add a 16 into the parenthesis, BUT we cannot disregard that 26 sitting out front there. It refuses to be ignored. It is still considered a multiplier. So what we are really adding on to the right side is 25*16 which is 400. 
which simplifies to 
. The standard form of an ellipse is 
if its horizontal axis is the transverse axis, or 
if its vertical axis is the transverse axis. Notice that the a and b moved as the difference between the 2 equations. A is always the larger value and dictates which ellipse you have, horizontal or vertical. Our equation has a 225 on the right, so we will divide both sides by 225 to get that much-needed 1 on the right: 
. Because 25 is larger than 9, this is a horizontal ellipse, our a value is the square root of 25 which is 5, and our b value is the square root of 9 which is 3. The center is (0, 4). You want the focus and now we can find it. The formula for the focus is 
where c is the distance from the center to the focus. We have an a and a b to find c: 
, which gives us that c=4. The focus is 4 units from the center and always lies on the transverse axis. It shares a y value with the center and moves from the x-coordinate of the center the value of c. Our center is (0, 4) so our y value of the focus is 4; our x coordinate of the center is 0, so the x value of the focus is 4. The coordinates of the focus are (4, 4).
True or false for 1 and 3
2 answers:
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Answer:
x ≈ 12.96
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 11² = 17²
x² + 121 = 289 ( subtract 121 from both sides )
x² = 168 ( take the square root of both sides )
x = ≈ 12.96 ( to the nearest hundredth )
Answer:
a)
b)
Step-by-step explanation:
<u>Coterminal angles</u> have the same terminal sides in standard position.
a) To find an angle between and
, that is coterminal with
, we keep adding multiples of
until we get an angle within the specified range.
.
In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive.
b) This time we want to find an that coterminal with radians.
We keep subtracting multiples of until we get an angle measure within the specified range.