Find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph.

Question

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph.

Answer 1

Step 1:

The conic equation .

The coefficients of and are the same sign and equal.So the equation is circle.

Standard form of circle is .

Where center is and  is radius.

Step 2:

Convert the circle equation standard form of circle.

Compare it to standard form of circle.

  and .

Step 3:

Find four points " radius away from the center in the up, down, left and right direction".

Up .

Down .

Left .

Right .

Graph:

Draw the coordinate plane.

Plot the center .

Plot the four points " radius away from the center in the up, down, left and right direction".

Sketch the circle.

Solution:

  and .