The a and b determine how big or small the shape of the conic section is.
<span>For the different conic sections given through the equations </span>
<span>Circle: x^2/a^2 + y^2/a^2=1 </span>
<span>Ellipse: x^2/b^2+y^2/a^2 = 1 </span>
<span>Hyperbola: x^2/a^2 - y^2/b^2 = 1 </span>
<span>When trying to isolate cos and sin from those equations to get cos^2t + sin^2 t = 1 you can determine the conic section when substituting cos t = x/a and sint = y/b into cos^2t+sin^2t square it and then refer to the conic section equations to determine the conic section. x defines the major axis and y is the minor axis. a and b provide the coordinate pairs</span>
Hey there! :D
First, find the slope.
m= (y2-y1)/(x2-x1) I'm using points (0,3) and (1,5)
m=(5-3)/(1-0)
m= 2/1
m=2
Now, plug that into point slope. Use point (1,5) m=2
y-y1= m(x-x1)
y-5= 2(x-1)
Distribute.
y-5=2x-2
Add 5 to both sides.
y=2x+3 == equation of the line in slope intercept form. y=mx+b
I hope this helps!
~kaikers
After solving ![\sqrt[5]{128x^8y^2}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B128x%5E8y%5E2%7D)
we get ![2x\sqrt[5]{4}\sqrt[5]{x^3}\sqrt[5]{y^2}](https://tex.z-dn.net/?f=2x%5Csqrt%5B5%5D%7B4%7D%5Csqrt%5B5%5D%7Bx%5E3%7D%5Csqrt%5B5%5D%7By%5E2%7D)
Step-by-step explanation:
We need to solve
Applying the rule: ![\sqrt[a]{xy}=\sqrt[a]{x}.\sqrt[a]{y}](https://tex.z-dn.net/?f=%5Csqrt%5Ba%5D%7Bxy%7D%3D%5Csqrt%5Ba%5D%7Bx%7D.%5Csqrt%5Ba%5D%7By%7D)
![\sqrt[5]{128x^8y^2}\\=\sqrt[5]{128}\sqrt[5]{x^8}\sqrt[5]{y^2}\\We\,\,know\,\,that\,\,128=2\times2\times2\times2\times2\times2\times2=2^7\,\,or\,\,2^5.2^2\\=\sqrt[5]{2^5.2^2}\sqrt[5]{x^5.x^3}\sqrt[5]{y^2}\\=(2^5)^{\frac{1}{5}}\sqrt[5]{2^2}\sqrt[5]{x^5}\sqrt[5]{x^3}\sqrt[5]{y^2}\\=2x\sqrt[5]{4}\sqrt[5]{x^3}\sqrt[5]{y^2}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B128x%5E8y%5E2%7D%5C%5C%3D%5Csqrt%5B5%5D%7B128%7D%5Csqrt%5B5%5D%7Bx%5E8%7D%5Csqrt%5B5%5D%7By%5E2%7D%5C%5CWe%5C%2C%5C%2Cknow%5C%2C%5C%2Cthat%5C%2C%5C%2C128%3D2%5Ctimes2%5Ctimes2%5Ctimes2%5Ctimes2%5Ctimes2%5Ctimes2%3D2%5E7%5C%2C%5C%2Cor%5C%2C%5C%2C2%5E5.2%5E2%5C%5C%3D%5Csqrt%5B5%5D%7B2%5E5.2%5E2%7D%5Csqrt%5B5%5D%7Bx%5E5.x%5E3%7D%5Csqrt%5B5%5D%7By%5E2%7D%5C%5C%3D%282%5E5%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%5Csqrt%5B5%5D%7B2%5E2%7D%5Csqrt%5B5%5D%7Bx%5E5%7D%5Csqrt%5B5%5D%7Bx%5E3%7D%5Csqrt%5B5%5D%7By%5E2%7D%5C%5C%3D2x%5Csqrt%5B5%5D%7B4%7D%5Csqrt%5B5%5D%7Bx%5E3%7D%5Csqrt%5B5%5D%7By%5E2%7D)
So, After solving we get
Keywords: Solving with Exponents
Learn more about Solving with Exponents at:
#learnwithBrainly
