## Description

It’s only 2 pages with 7 questions 4 multiple choices and 3 graphing questions

### Unformatted Attachment Preview

Purchase answer to see full attachment

## Explanation & Answer

Done.Here's the solution file (both in doc and pdf format).😊

Name the conic. If the conic is a circle then indicate circle and not ellipse for

the answer.

(1) 4𝑥 2 + 8𝑥 − 5𝑦 2 − 15𝑦 = 2

A) Parabola

B) Ellipse

(2) 4𝑥 2 + 12𝑥 + 6𝑦 2 − 12𝑦 = 24

C) Hyperbola

D) Circle

A) Parabola

B) Circle

2

(3) 𝑦 − 7𝑦 = 3𝑥 + 12

C) Ellipse

D) Hyperbola

A) Circle

B) Ellipse

2

2

(4) 5𝑥 + 9𝑥 + 5𝑦 − 9𝑦 = 15

C) Parabola

D) Hyperbola

A) Circle

B) Hyperbola

C) Parabola

D) Ellipse

(5) Find the vertex, focus, directrix and endpoints of the latus rectum. Graph

the equation.

(𝑦 − 2)2 = −8(𝑥 + 1)

Sol: Vertex:

The parabola having vertex (h, k) in standard form is

(𝑦 − 𝑘)2 = 4𝑝(𝑥 − ℎ)

To find the vertex (h, k), we need to write the equation in standard form of

parabola. So,

(𝑦 − 2)2 = 4(−2)(𝑥 − (−1))

Comparing the equation with standard form equation, we have

ℎ = −1, 𝑘 = 2, 𝑝 = −2

Hence

Vertex = (−1, 2)

Directrix:

The parabola of the form

(𝑦 − 𝑘)2 = 4𝑝(𝑥 − ℎ)

has the directrix 𝑥 = ℎ − 𝑝.

To find the directrix, we again need to write the equation of parabola in

standard form which is

(𝑦 − 2)2 = 4(−2)(𝑥 − (−1))

Comparing the equations, we get

ℎ = −1, 𝑘 = 2, 𝑝 = −2

So, to find the directrix, we use the equation 𝑥 = ℎ − 𝑝 for this form of

parabola,

𝑥 = ℎ− 𝑝

Putting the values, we get

𝑥 = −1 − (−2)

𝑥 = −1 + 2

𝑥=1

Hence the directrix is 𝑥 = 1

Endpoints of the latus rectum:

First, we need to find the focus.

The focus of parabola of the form

(𝑦 − 𝑘)2 = 4𝑝(𝑥 − ℎ)

is (h+p, k)

Considering the equation again in standard form, we get

(𝑦 − 2)2 = 4(−2)(𝑥 − (−1))

Here, ℎ = −1, 𝑘 = 2, 𝑝 = −2

So, putting the values, we have the focus

(−1 + (−2),2)

(−1 − 2,2)

(−3,2)

To find the end points of latus rectum, we need to know the length of latus

rectum. The length of latus rectum is |4p|.

So, the length of latus rectum is

𝑙 = |4𝑝| = |4(−2)| = | − 8| = 8

Now, the endpoints of latus rectum for this type of parabola can be found

using the focus point as

𝑙

8

2

2

First endpoint can be found by moving = = 4 units up in the direction of

positive y axis from y coordinate of the focus and second point can be found

moving 4 unit down in the direction of negative y axis. So,

𝑃𝑜𝑖𝑛�...

### Review

### Review

## 24/7 Homework Help

Stuck on a homework question? Our verified tutors can answer all questions, from basic **math** to **advanced rocket science**!

## Similar Content

## Related Tags

### To the Lighthouse

by Virginia Woolf

### The Joy Luck Club

by Amy Tan

### Breakfast at Tiffanys

by Truman Capote

### The 5 Love Languages

by Gary Chapman

### Harry Potter and the Sorcerers Stone

by J. K. Rowling

### The Catcher in the Rye

by J. D. Salinger

### Cant Hurt Me - Master Your Mind and Defy the Odds

by David Goggins

### The Dispossessed

by Ursula Kroeber Le Guin