Question

1) There is a solution to x = -(y-5)^2 and x = (y -5 )^2 + 7
a) true
b) false

2) There is no real solution to y = -1 and y = x^2 + 9
a) true
b) false

3) the vertex of the graph of y = 3(x+ 9)^2 + 5 is a minimum value ?
a) true
b) false

4)find the center and radius of the circle with the given equation x^2 + y^2 + 6y = -50 -14x

5) sketch the graph of y = (x+2)^2 - 1
6) sketch the graph of 9x^2 + 4y^2 = 36
7) sketch the graph of (y - 1)^2 /9 - (x+2)^2 /4 = 1
8) solve the system, x^2/16 + y^2/4 less than or equal to 1 and y > 1x/2 -2

Can some one assist me with these ? I'm lost here,

Answer 1

1 False.

2. True.

3. True.

4. X^2 + Y^2 + 6Y = - 50 - 14X,
Complete the square:
X^2+14X+(14/2)^2+Y^2+6Y+(6/2)^2=-50,
X^2+14X+49+Y^2+6Y+9 = -50+49+9,
X^2+14X+49+Y^2+6Y+9 = 8,
Factor the perfect squares:
(X+7)^2+(Y+3)^2 = 8 = r^2,

C(-7,-3).

r = sqrt8 = 2.83

5. Y = (X+2)^2-1.
Graph the given Eq using the selected points listed below:

(-4,3), (-3,0), V(-2,-1), (-1,0),(0,3).

6. 9X^2+4Y^2 = 36,
Divide both sides by 36:
X^2/4+Y^2/9 = 1, Y-Elipse.
Graph the elipse using the points listed below:
(-2,0), (2,0), (0,-3), (0,3).