Scribd
Upload
335 views2 pages

Quiz 1 & 2

This document contains two quizzes on circle and parabola equations. Quiz 1 involves finding standard forms of circles, changing forms between general and standard, and finding equations given properties. Quiz 2 is similar but for parabolas, involving finding standard forms, changing forms, and finding equations given foci, directrixes, and vertices. Both quizzes contain bonus problems applying concepts of circles and parabolas.

Uploaded by

L Alcosaba
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
335 views2 pages

Quiz 1 & 2

This document contains two quizzes on circle and parabola equations. Quiz 1 involves finding standard forms of circles, changing forms between general and standard, and finding equations given properties. Quiz 2 is similar but for parabolas, involving finding standard forms, changing forms, and finding equations given foci, directrixes, and vertices. Both quizzes contain bonus problems applying concepts of circles and parabolas.

Uploaded by

L Alcosaba
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

QUIZ 1 – CIRCLE (25 pts)

A. 5pts each. Find the standard form (1) of the following. State the coordinates of the
center (1), length of radius (1). Then, sketch the graph (2).
1. 𝑥 2 + 𝑦 2 − 6𝑥 − 2𝑦 − 6 = 0
2. 4𝑥 2 + 4𝑦 2 + 4𝑥 − 12𝑦 + 1 = 0
3. 𝑥 2 + 𝑦 2 = 5
B. 2 pts each. Change the following to general form.
1. (𝑥 + 3)2 + (𝑦 + 4)2 = 16
3 2 1 2
2. (𝑥 − 5) + (𝑦 − 3) = 10
C. 2pts each. Find the equation of the circle given the following conditions.
1. Center at (2,1), radius is 3
2. Tangent to the x-axis at (2, 0), radius 3.
3. Ends of diameter at (2,-1) and (-2, 3).
D. BONUS 5pts. Find the equation of the circle with points (2𝑎, 0) and (0,2𝑏) as ends of
the diameter.
QUIZ 2 – PARABOLA (30pts)
A. 7 pts each. Find the standard form (1) of the following. State the center (1), vertex (1),
focus (1), equation of directrix (1). Then, sketch the graph (2).
1. 𝑦 2 + 8𝑥 + 8 = 0
2. 𝑥 2 − 8𝑥 − 6𝑦 − 8 = 0
3. 𝑦 2 − 4𝑦 + 8𝑥 − 28 = 0
B. 2pts each. Change the following to general form.
1. (𝑥 − 3)2 = −24(𝑦 + 2)
2. (𝑦 + 2)2 = 8(𝑥 − 4)
C. 2pts each. Find the equation of the circle given the following conditions.
1. Vertex at (3,2) and focus at (3,4)
2. Vertex at (4,1), x=2 as equation of directrix
3. Focus at (-2, 2), y=4 as equation of directrix.
D. BONUS 5pts. Derive the equation of the set of all points that is equidistant from the
point (0, a) and the line y= -a.

You might also like