graphing help ugh.?

Question

What would the graph of the following equation of a conic section look like?

x^2/9 + y^2/25 = 1

Would it be vertical ellipse, horizontal ellipse, vertical hyperbola, or horizontal hyperbola?



Describe the graph of the following equation:
(x-2)^2/36 + (y-1)^1/36 = 1
Would it be circle with the center in the first quadrant with radius 6, circle with center in the second quadrant with radius 36, circle with center in the third quadrant with raduis 6, or circle with center in the fourth quadrant with radius 36?


Given the equation of the ellipse below, find the local points.

x^2/25 + Y^2/9 = 1
Would it be (5,0) and (-5,0), (4,0) and (-4,0), (0,3) and (0,-3), or (5.83,0) and (-5.83,0)?


Please help me and give me the RIGHT answers. This is a pretest im suppose to do. ive done this class before, but i failed it, and im already suppose to know this stuff im guessing. but i dont. and i need help cause i need to pass this please please please help.

Answer 1

x²/9 + y²/25 = 1 is an ellipse (hyperbolas have a minus sign in the middle). The horizontal semi-axis is √9 = 3 and the vertical semi-axis is √25 = 5. Since the vertical semi-axis is larger, it's a vertical ellipse.

(x-2)²/36 + (y-1)²/36 = 1 (that's what you meant, right?)

is a circle of radius √36 = 6 with center at (2,1). The point (2,1) is in the first quadrant.

x²/25 + y²/9 = 1

The horizontal semi-axis is √25 = 5 and the vertical semi-axis is √9 = 3 so this is a horizontal ellipse. Because the equation of the ellipse is equivalent to (x-0)²/25 + (y-0)²/9 = 1, the center of the ellipse (where the horizontal and vertical axes intersect) is at (0,0)

The foci lie on the line containing the semi-major axis, which is the larger of the horizontal semi-axis and the vertical semi-axis. (Similarly, the smaller of these two is called the semi-minor axis.) Let a denote the length of the semi-major axis, let b denote the length of the semi-minor axis, and let c denote the distance from either focus to the center of the ellipse. Then

c² = a² - b²

So for this ellipse, c² = 25 - 9 = 16, so c = 4. The foci are located 4 units from the center, on the major axis. So the coordinates of the foci are (4,0) and (-4,0)

Answer 2

If the numbers under x^2 and y^2 are different but with the same sign, you have an ellipse.The variable with the bigger number under it, that's the way it goes. So it's a vertical ellipse.

The next one, see that both have 36 on bottom. When it's the same, you have a circle. The center is the values you'd put on top to make the tops be zero so here that's (2,1) and the radius (if the equation is equal to 1) is the square root of the bottom (6).

As for local points, is that the vertices (outer ends)? It looks so by the answer choices. Just see what makes the top equal the bottom, and make the other variable zero. So 5 or -5 for x [and 0 for y], or 3 or -3 for y [and 0 for x]

If you want more details I can explain. Send an IM

Answer 3

hiya The shaded region represents the achieveable strategies on your equation. What I advise by employing it relatively is that the shaded region is the section the place you're greater in all probability to discover a answer on your question.