## Unofficialllyy one year ago Will fan and medal!!

1. Unofficialllyy

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 2x + y2 + 4y = 20

2. Unofficialllyy

$x^2+2x+y^2+4y=20$

3. Unofficialllyy

@welshfella

4. Unofficialllyy

I know I have to complete the square but I have no clue how to do it.

5. welshfella

convert it to the form (x - a)^2 + (y - b)^2 = r^2 complete the square x^2 + 2x and y^2 + 4y

6. Unofficialllyy

We use (h-k)^2+(y-k)^2=r^2 but it's the same thing as the form you gave me.

7. welshfella

x^2 + 2x + y^2 + 4y = 20 (x + 1)^2 - 1 + (y + 2)^2 - 4 = 20 to complete the square you take half of the coefficient of x then you have to subtract this value squared (x + 1)^2 = x^2 + 2x + 1 - so you have to subtract 1^2 from this to make x^2 + 2x

8. welshfella

(x + 1)^2 + (y + 2)^2 = 20+1 + 4 = 25 so if you compare this with the general equation you'll see that center = (-1,-2) and radius = sqrt25 = 5

9. Unofficialllyy

Thank you so much. I have one more question if you dont mind?

10. welshfella

well i must go in 10 minutes so we'll see how much i can do in that time

11. Unofficialllyy

Prove that the two circles shown below are similar.

12. Unofficialllyy

I know that all circles are similar, but how do I prove it?

13. welshfella

oh must go now I'm sure jhannybean can help

14. Unofficialllyy

Okay thank you!

15. Jhannybean

$x^2 + 2x + y^2 + 4y = 20$$(x^2+2x) + (y^2+4y)=20$$(x^2+2x+\color{red}{1}) +(y^2+4y+\color{red}{4})=20+\color{red}{1}+\color{red}{4}$$(x+1)^2+(y+2)^2=25~~~\checkmark$

16. Jhannybean

Haha you dont have to @welshfella

17. Unofficialllyy

@Jhannybean Could you help with the circle question? It's my last one. :/

18. Jhannybean

hint: try creating triangles within the circles and then using their ratios in comparison.

19. Jhannybean

|dw:1440188772500:dw|

20. Unofficialllyy

So once i have the ratios what do i do?

21. Jhannybean

If we compare al the sides in a ratio, we would see it has a proportional relationship

22. Jhannybean

First find the hypotenuse of both triangles, the smaller triangle having a hypotenuse of x. and the bigger one having hypotenuse of y. $c_1 : x^2= 2^2+2^2 = 8 \iff x=\sqrt{8}$$c_2 : y^2=5^2+5^2 = 50 \iff y=\sqrt{50}$

23. Unofficialllyy

What about dilations? Couldn't we see if they are similar that way?

24. Jhannybean

Then we can say by the SSS theorem, $\frac{2}{5} = \frac{\sqrt{8}}{\sqrt{50}}$

25. Jhannybean

Hmm..i'm not really familiar with dilations! sorry.

26. Unofficialllyy

Okay well thank you!

27. Jhannybean

@cwrw238 could you help me understand dilations? :)

28. Unofficialllyy

I understand the way you did it, and it makes perfect sense, so no worries. :) thank you for your help!

29. Jhannybean

Oh cool! no problem.