Solev for x and y:
- x^2=4y+13
- ((x-.56)^2)/.4+((y+.39)^2)/1.6=.5
- x^2+4x-2.52
- ((y+.8)^2)/.2-((x+0)^2)/1=1
Can someone solve these because i wasnt able to find the answers for like an hour:(
not clear what you mean by solve for x and y,
1. x^2=4y+13
is a parabola, which can be arranged as y = (1/4)x^2 - 13/4
or x = ±√(4y + 13)
2. (x-.56)^2/.4 + (y+.39)^2/1.6 = .5
an ellipse centre at (.56, -.39) , with a^2 = .2 and b^2 = .8
3. x^2+4x-2.52 , not even an equation, if it is equal to y, you have another parabola
4. (y+.8)^2/.2 - (x+0)^2/1 = 1 <---- a hyperbola
If you want the x- and y-intercepts, just plug in y=0 or x=0 and solve for x or y.
To solve these equations, we'll go through each one step by step.
1. x^2 = 4y + 13
To solve for x, isolate it by moving the terms involving x to one side:
x^2 - 4y = 13
This equation doesn't provide enough information to solve for both x and y. It represents a parabola in the x-y plane.
2. ((x - 0.56)^2) / 0.4 + ((y + 0.39)^2) / 1.6 = 0.5
To solve this equation, we'll simplify it step by step:
First, multiply both sides of the equation by 0.4 and 1.6 to eliminate the denominators:
0.4 * ((x - 0.56)^2) + 1.6 * ((y + 0.39)^2) = 0.5
Next, distribute and simplify:
0.4x^2 - 0.448x + 0.06336 + 1.6y^2 + 1.248y + 0.38976 = 0.5
Rearrange the equation and combine like terms:
0.4x^2 + 1.6y^2 - 0.448x + 1.248y + 0.45312 = 0
This equation represents an ellipse in the x-y plane.
3. x^2 + 4x - 2.52
This is a quadratic equation. To solve it, we'll set it equal to zero and factor or use the quadratic formula:
x^2 + 4x - 2.52 = 0
Since factoring might be difficult, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the quadratic equation, a = 1, b = 4, and c = -2.52. Plugging in these values:
x = (-4 ± √(4^2 - 4 * 1 * -2.52)) / (2 * 1)
Simplifying:
x = (-4 ± √(16 + 10.08)) / 2
x = (-4 ± √26.08) / 2
Calculating the square root:
x = (-4 ± √26.08) / 2
x = (-4 ± 5.105) / 2
Simplifying further:
x = (-4 + 5.105) / 2 or x = (-4 - 5.105) / 2
Simplifying again:
x = 0.5525 or x = -4.5525
Thus, the solutions for x are x = 0.5525 or x = -4.5525.
4. ((y + 0.8)^2) / 0.2 - ((x + 0)^2) / 1 = 1
To solve this equation, we'll simplify it step by step:
First, multiply both sides of the equation by 0.2 and 1 to eliminate the denominators:
0.2 * ((y + 0.8)^2) - ((x + 0)^2) = 1
Next, distribute and simplify:
0.2y^2 + 0.32y + 0.128 - x^2 = 1
Rearrange the equation and combine like terms:
0.2y^2 + 0.32y - x^2 - 0.872 = 0
This equation represents a parabola in the x-y plane.
In summary, the first equation represents a parabola, the second equation represents an ellipse, the third equation is a quadratic equation, and the fourth equation represents another parabola.