Question

Select the correct equations in the image.

Answer 1

Answer:

The equations of the parabolas whose focus and vertex lie in different quadrants are;

The third equation $x=-\frac{y^{2}}{16}-\frac{y}{4}+\frac{11}{4}$ and the sixth equation$y=-\frac{x^{2}}{24}-\frac{5x}{12}+\frac{95}{24}$

Step-by-step explanation:

We analyse each of the equations as follows

$h =\frac{-b}{2a}$

$k = \frac{4ac-b^2}{4a}$

Vertex = V(h, k)

Focus = F(h, k+p)

First equation

a = -1/8

b = 1/4

c = 23/8

k = 3

h = 1 Hence same quadrant

Second equation

a = 1/32

b = 1/4

c = -13/2

h = -4

k = -7 same quadrant

Third equation

a = -1/16

b = -1/4

c = 11/4

k = 3

h = -2 Hence different quadrants

Fourth equation

a = 1/16

b = 1/4

c = -19/4

h = -2

k = -5 The same quadrant

Fifth equation

a = -1/36

b = -5/18

c = 299/36

k = 620.56

h = 149.5 The same quadrant and

Sixth equation

a = -1/24

b = -5/12

c = 95/24

h = -5

k ≈ 5   Hence different quadrants

Hence the equations of the parabolas whose focus and vertex lie in different quadrants are the third and sixth equations presented as follows;

Third equation:

$x=-\frac{y^{2}}{16}-\frac{y}{4}+\frac{11}{4}$

Sixth equation:

$y=-\frac{x^{2}}{24}-\frac{5x}{12}+\frac{95}{24}$.