The point T(-1,4) lies on the ellipse on the graph.
The equation of the ellipse in generalform is:
(x/√2)² + (y/√6)² = 1
An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The given equation, 4y² + 12x² = 24, can be simplified by dividing both sides by 24 to get:
y²/6 + x²/2 = 1
This is the equation of an ellipse centered at the origin, with a horizontal majoraxis of length 2√6 and a vertical minoraxis of length 2√2.
To identify the graph of the ellipse passing through T(-1,4), we substitute x = -1 and y = 4 in the equation and simplify:
4(4)² + 12(-1)² = 24
64 - 12 = 52
Thus, point T(-1,4) lies on the ellipse.
To find the equation of the translated or rotated ellipse in general form, we can use standard transformations.
Let (h,k) be the center of the ellipse.
Then we have:
(x-h)²/a² + (y-k)²/b² = 1
where a and b are the lengths of the semi-major and semi-minor axes, respectively.
The center of the given ellipse is (0,0), so h = 0 and k = 0.
To determine the values of a and b, we note that a^(2) is the coefficient of x² in the equation, and b² is the coefficient of y².
Thus, we have:
a² = 2 and b² = 6
Taking squareroots, we get:
a = √2 and b = √6
Therefore,
The equation of the ellipse in generalform is:
(x/√2)² + (y/√6)² = 1
This is the equation of an ellipse with a horizontal majoraxis of length 2√2 and a vertical minoraxis of length 2√6, centered at the origin and rotated counterclockwise by an angle of θ such that tan(2θ) = 4/3.
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Answer:
b. ellipse; 3x^2 + y^2 + 6x - 8y + 13 = 0
Step-by-step explanation:
thats the answer on edg :)
B. y-2=1/3(x-6)
C. y-2=3(x-6)
D. y-6=-3(x-2)
E. y-2=-3(x-6)
Answer:
Step-by-step explanation:
The slope of the perpendicular line m₂ must be the negative reciprocal of the slope m₁ of the first line.
The only equation with m = 3 is
This is the point slope form of the equation for a straight line through (6, 2) with slope = 3.
Answer:
C
Step-by-step explanation:
then
the answer is 12 since the sum of the two angles has to equal 180.
first you do
5x+5+115=180
combine like terms
5x+120=180
subtract 120
5x=60
then divide by 5
x=12
She needs only 3 cups of sugar.
Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.
A muffin recipe calls for 4 cups of sugar and yields 36 muffins.
That means one cup of sugar yields 36 / 4 = 9 muffins.
So if we only need 24 muffins then
= 24 / 9
< 3
Therefore, Amelia needs only 3 cups of sugar to yield 24 muffins.
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Answer:
4 is place value of 4.
Step-by-step explanation:
Given : 4.735
To find : What is the place value for 4
Solution : We have given 4.735
We can see 4 is at ones place = 4 *1
and 7 is at tenth place 3 is at hundredth place , 5 is at thousandth place.
So, the place value of 4 is 4
Therefore, 4 is place value of 4.