# Need Help with a Few Basic Problems Please

• Feb 17th 2013, 03:44 PM
StephenSkinner
Need Help with a Few Basic Problems Please
1. Determine if the graph of the equation y = 16 - x^2 is symmetric with respect to:

a) the x-axis (yes or no, w/ brief explanation)
b) the y-axis (yes or no, w/ brief explanation)
c) the origin (yes or no, w/ brief explanation)
d) Find the x-intercept(s).
e) Find the y-intercepts(s).

2. Given the equation of a circle, find the center and the radius.

x^2 + y^2 + 5x - 2y + 6 = 0

3. Write the equation in general form of the line that contains the point (7,3) and is parallel to the line passing through the points (1,1) and (-1,5).

Any help is appreciated, thanks!
• Feb 17th 2013, 06:21 PM
Re: Need Help with a Few Basic Problems Please
definitions

A function is symmetric about the x-axis if and only if replacing y with -y will yield the same function (explain why)
A function is symmetric about the y-axis if and only if replacing x with -x will yield the same function (explain why)
A function is symmetric about the origin if and only if it is both symmetric about the x and y axis

x-intercepts are points which lie on the line y = 0. find where y= 16-x^2 and y = 0 intersect
y-intercepts are points which lie onthe line x = 0. find where y = 16-x^2 and x = 0 intersect

2. You can re-write the equation by rearranging and grouping terms, and then completing the square for both x and y

x^2 + 5x + y^2 - 2y + 6 = x^2 + 5x + (5/2)^2 -(5/2)^2 + y^2 - 2y + 1 - 1 + 6 = (x+(5/2))^2 + (y+1)^2 + -(5/4) = 0

Hence the equation can be re-written as (x+(5/2))^2 + (y+1)^2 = (5/4) In this form, can you tell me what the center and radius is? If you have a problem with completing the square let me know.

3.
To be parallel with a line means having the same slope. calculate the slope of the line through the points (1,1) and (-1,5) using $\displaystyle m = \frac{y_1 - y_0}{x_1 - x_0}$ (rise over run)
Using m and the point (7,3) plug them into the point slope form $\displaystyle y-y_1= m(x-x_1)$ which is just rewriting the above slope formula to get the equation for your desired line.
• Feb 18th 2013, 03:27 PM
StephenSkinner
Re: Need Help with a Few Basic Problems Please

For #1, I got:

a) no
b) yes
c) no
d) x-int = 4, -4
e) y-int = 16

#2:

center = (-5/2 , -1)