Question

Help please on these 2 questions

Answer 1

you'll have to complete the square on the x-terms and y-terms, are you familiar with how to do this?

Answer 2

NO :/

Answer 3

start by isolating the x terms

x^2 - 8x

now, take the b-coefficient (-8), divide by 2, then square it - what do you get?

Answer 4

-8/2=-4
2i

Answer 5

square it not take the square root

Answer 6

-4^2

Answer 7

be careful with parentheses

(-4)^2 = ?

Answer 8

16

Answer 9

good, so we add 16 to both sides of the equation

now that we have (x^2 - 8x + 16) factor this into a squared binomial

Answer 10

(x-4)^2

Answer 11

good, now we repeat this w/ the y terms

y^2 +10y

again, take the b-term, divide it by 2, square it, add it to both sides of the eqn, then factor

Answer 12

10/2=5
5^2

Answer 13

25

Answer 14

good, then factor y^2 + 10y + 25

Answer 15

(y+5)^2

Answer 16

good, so far we have

(x-4)^2 + (y+5)^2 = 16 + 25 = 41

now, divide both sides by 41 to get it into standard form

(x-4)^2 / 41 + (y+5)^2 / 41 = 1

what conic is this? take a look at the thing I posted at the beginning

Answer 17

ellipse

Answer 18

awesome

now, looking at the ellipse equation where the center is (h,k) what's the coordinates of the center?

Answer 19

(not a hyperbola, we have a + sign not a - sign in the middle)

Answer 20

(4,-5)

Answer 21

other way around with the signs

Answer 22

okay so (-4,5)

Answer 23

anyway for #2 try completing the square w/ the y terms and re-arranging the equation for x

Answer 24

y^2 +4y, complete the square

Answer 25

the second equation is not an ellipse or hyperbola (no x^2 term) so it has to be written in the form x = a(y-k)^2 + h

Answer 26

the -8(x-2) one?