# Problems in Analytic Geometry

Please help on how to approach the following problems:

1. For the given equation, list the intercepts and test for symmetry

x^2+4y^2=4

What are the intercepts?

2. For the given equation, list the intercepts and test for symmetry.

y=negative7x/x^2+25

What are the intercepts?

3. If (a, negative 6) is a point on the graph of y=x^2-5x what is a?

4. Find an equation for the line with the given properties. Express teh equation in slope intercept form.

Containng the points P=(- 4,-4) and Q = (-2, -1)

What is the equation of the line?

5. Find the equation of a line that is perpendicular to the line y=1/2x+3 and contains the point (-8,0)

y=?

https://brainmass.com/math/analytic-geometry/listing-intercepts-testing-symmetry-480280

#### Solution Preview

1. x^2 + 4y^2 = 4 is the equation of an ellipse. The standard form of this equation is (x/2)^2 + y^2 = 1. Thus we see that this is an ellipse centered at the origin with semimajor axis of length 2 and semiminor axis of length 1 oriented along the x and y axes respectively. The intercepts of this ellipse ...

#### Solution Summary

The solution solves several problems in analytic geometry.