Math help please

[uga75]

Hello, i need help trying to solve these problems, dont understand how to arrive to answers... thak you very much in advance..


Solve-
1)4x^2+9y^2-16x+18y-11=0

2) y^2= -20x vertex foci

3) Sin^2x-sinx= 0

 

[chrisr]

Well that first one is the equation of an ellipse.

The equation of a circle is (x-h)[sup:3ec2pi6n]2[/sup:3ec2pi6n]+(y-k)[sup:3ec2pi6n]2[/sup:3ec2pi6n]=r[sup:3ec2pi6n]2[/sup:3ec2pi6n].
The equation of an ellipse is (x-h)[sup:3ec2pi6n]2[/sup:3ec2pi6n]/a[sup:3ec2pi6n]2[/sup:3ec2pi6n]+(y-k)[sup:3ec2pi6n]2[/sup:3ec2pi6n]/b[sup:3ec2pi6n]2[/sup:3ec2pi6n]=1.

Your equation is the "multiplied out" version of this.

(b[sup:3ec2pi6n]2[/sup:3ec2pi6n]/b[sup:3ec2pi6n]2[/sup:3ec2pi6n])(x-h)[sup:3ec2pi6n]2[/sup:3ec2pi6n]/a[sup:3ec2pi6n]2[/sup:3ec2pi6n]+(a[sup:3ec2pi6n]2[/sup:3ec2pi6n]/a[sup:3ec2pi6n]2[/sup:3ec2pi6n])(y-k)[sup:3ec2pi6n]2[/sup:3ec2pi6n]/b[sup:3ec2pi6n]2[/sup:3ec2pi6n]=1.
b[sup:3ec2pi6n]2[/sup:3ec2pi6n](x-h)[sup:3ec2pi6n]2[/sup:3ec2pi6n]/(ab)[sup:3ec2pi6n]2[/sup:3ec2pi6n]+a[sup:3ec2pi6n]2[/sup:3ec2pi6n](y-k)[sup:3ec2pi6n]2[/sup:3ec2pi6n]/(ab)[sup:3ec2pi6n]2[/sup:3ec2pi6n]=1.
b[sup:3ec2pi6n]2[/sup:3ec2pi6n](x-h)[sup:3ec2pi6n]2[/sup:3ec2pi6n]+a[sup:3ec2pi6n]2[/sup:3ec2pi6n](y-k)[sup:3ec2pi6n]2[/sup:3ec2pi6n]=(ab)[sup:3ec2pi6n]2[/sup:3ec2pi6n].

4x[sup:3ec2pi6n]2[/sup:3ec2pi6n]+9y[sup:3ec2pi6n]2[/sup:3ec2pi6n]-16x+18y-11=0 is 4(x-h)[sup:3ec2pi6n]2[/sup:3ec2pi6n]+9(y-k)[sup:3ec2pi6n]2[/sup:3ec2pi6n]=4(9)=36.

4x[sup:3ec2pi6n]2[/sup:3ec2pi6n]-8xh+4h[sup:3ec2pi6n]2[/sup:3ec2pi6n]+9y[sup:3ec2pi6n]2[/sup:3ec2pi6n]-18ky+9k[sup:3ec2pi6n]2[/sup:3ec2pi6n]=36.

Can you find h and k now ?

The second one is (y-0)[sup:3ec2pi6n]2[/sup:3ec2pi6n]=-20(x-0) a parabola.
Try to find the vertex and focus now.

For the third one, you can try a few ways, but you haven't stated a domain.

Sin[sup:3ec2pi6n]2[/sup:3ec2pi6n]x-Sinx=0 is Sinx(Sinx-1)=0,
so Sinx is 0 or 1.
Can you "inverse Sine" those, or find the y co-ordinate on the unit circle circumference
corresponding to those and deduce the angle x?

 

[fasteddie65]

)4x^2 + 9y^2 - 16x + 18y - 11 = 0
4x^2 - 16x + 9y^2 + 18y = 11
4(x^2 - 4x) + 9(y^2 + 2y) = 11
4(x^2 - 4x + 4) + 9(y^2 + 2y + 1) = 11 + 16 + 9
4(x - 2)^2 + 9(y + 1)^2 = 36
(x - 2)^2/9 + (y + 1)^2/4 = 1
This is an ellipse, with center (2, -1), major axis of length 6, minor axis of length 6. It is elongated horizontally.

2) y^2 = -20x vertex foci
(y - 0)^2 = -20(x - 0)
Vertex (0, 0)
4p = -20
p = -5
Focus is (-5, 0). It opens to the left.

3) sin^2 x - sin x = 0
sin x(sin x - 1) = 0
sin x = 0 or sin x - 1 = 0
x = 0, ? or sin x = 1
x = ?/2