How can I solve 3*x^2+y^2=300?
I do not know what you mean by "solve".
This is an ellipse
x^2/1 + y^2/(sqrt 3)^2 = 10^2
x^2/10^2 + y^2/(10 sqrt 3)^2 = 1
center at(0,0)
total length along x axis = 2 * 10 = 20
total length along y axis = 2 * 10 sqrt 3 = 20 sqrt 3
i am expressing it as an equation. solve for x and y.
well, solve for y for example.
Since it is an ellipse centered at the origin, we know that for every x we better get a positive and a negative value of y
y^2 = 300 - 3 x^2
y = + or - sqrt (300 - 3 x^2)
Thank you.
To solve the equation 3*x^2 + y^2 = 300, you can use a couple of methods. One way is by rearranging the equation and solving for one variable in terms of the other.
1. Rearrange the equation:
3*x^2 + y^2 = 300
Subtract y^2 from both sides:
3*x^2 = 300 - y^2
Divide both sides by 3:
x^2 = (300 - y^2) / 3
2. Solve for x:
To isolate x, take the square root of both sides:
x = ±√[(300 - y^2) / 3]
Now, you have the equation for x in terms of y. This equation allows you to find the corresponding x values for different y values that satisfy the original equation.
Similarly, you can solve for y by rearranging the equation:
1. Rearrange the equation:
3*x^2 + y^2 = 300
Subtract 3*x^2 from both sides:
y^2 = 300 - 3*x^2
2. Solve for y:
To isolate y, take the square root of both sides:
y = ±√(300 - 3*x^2)
Now, you have the equation for y in terms of x. This equation allows you to find the corresponding y values for different x values that satisfy the original equation.
To summarize, the solutions to the equation 3*x^2 + y^2 = 300 can be found by using the equations x = ±√[(300 - y^2) / 3] and y = ±√(300 - 3*x^2). By substituting different values for x or y, you can obtain corresponding values for the other variable that satisfy the equation.