Question

Show that the equation represents a circle by rewriting it in standard form.
4x2 + 4y2 + 8x − y = 0

Answer 1

Complete the square on x and y respectively. Might want to divide through by 4 to eliminate the coefficients of x^2 and y^2 first.

Answer 2

divide it first y 4 so that the coefficient of x^2 and y^2 will be one

Answer 3

but i won't have a radius since it =0, so then what?

Answer 4

Gotta have faith :-)

Answer 5

You will by the time the dust settles on the algebra.

Answer 6

faith isn't going to finish my hw-_- haha

Answer 7

Seriously, when you complete the square, don't you end up adding stuff to both sides? That's going to give you your radius.

Answer 8

oooooh i see now!

Answer 9

Got an answer for me to check?

Answer 10

(x-1)^2+(y+1/8)^2=65/64 ?

Answer 11

Very close! \[(x+1)^2 + (y-\frac{1}8)^2 = \frac{65}{64}\]

Answer 12

You should look at your work again and figure out how you got your signs switched around.

Here's what I did:

\[4x^2+4y^2+8x-y=0\]Divide through by 4\[x^2+y^2+2x-\frac{y}{4} = 0\]Rearrange the \(x\) stuff first:
\[(x^2+2x) + (y^2 - \frac{y}4) = 0\]We take half of the coefficient of \(x\), square it, and add to both sides:
\[(x^2+2x+(\frac{2}{2})^2) + (y^2-\frac{y}4) = (\frac{2}{2})^2\]Rewrite the \(x\) terms as a perfect square\[(x+1)^2 + (y^2-\frac{y}4) = 1\]Take half of the coefficient of \(y\), square it, and add to both sides:\[(x+1)^2 + (y^2-\frac{y}4 + (-\frac{1}{8})^2) = 1+(-\frac{1}8)^2\]Rewrite the \(y\) terms as a perfect square:\[(x+1)^2 + (y-\frac{1}{8})^2 = 1+\frac{1}{64}\]

Answer 13

oh okay i found where i mixed them. thank you so much! can you help me with another? how would I find the area of this triangle if it isn't a right triangle?

Answer 14

Area of a triangle is given by \[A = \frac{1}{2}bh\]where \(b\) is the length of the base and \(h\) is the height. Works even for a weird triangle like this one. What's the length of the base? What's the height?

Answer 15

so 1/2*8*3?

Answer 16

Yep. And you could also do it by "extending" the triangle so that it had a vertex at (7,1) instead of at B, find the area of that triangle (1/2 * 9*3 = 27/2 = 13.5), then subtract off the little triangle added by doing so (1/2 * 1*3 = 1.5) and you get the same answer.

Answer 17

oh okay! okay so for this one, the equation is
x2/9+ y2/4= 1

Answer 18

Find the x- and y-intercepts.

Answer 19

Yes, that's the equation for that ellipse. The x and y intercepts are found by setting y and x = 0 respectively and solving for the remaining variable.

Answer 20

My cat is demanding that I go to bed now, it's cold in the house and she wants a warm body to snuggle with :-)

Answer 21

nooo don't leave me! can you help me with one more pweeeease

Answer 22

Okay, it'll have to be quick :-)

Answer 23

okay! simplify the compound fraction:
9x-9y/x/y+y/x

Answer 24

Can you write that with parentheses so I can tell what it is supposed to be?