Q 39. - Precalculus Enhanced with Graphing Utilities

Question

Describe each of the following graphs in the $xy$plane. Give justification.

(a) $x=0$     (b) $y=0$

(c) $x+y=0$ (d) $xy=0$

(e) $x^2+y^2=0$

Step-by-Step Solution

Answer

(a) $x=0$ is the equation of $y$ axis if we plot $x=0$ all the points will lie on $y$ axis.

(b) $y=0$ is the equation of $x$ axis if we plot graph all the points lie on $x$ axis.

(c) $x+y=0$ stated that every $y$ co-ordinate is the negative corresponding $x$-coordinate.

(d) $xy=0$ represents a pair of parallel lines.

(e) $x^2+y^2=0$ represents an ellipse.

Step 1. Justification for part (a).

Given information $x=0$ is the equation of $y$ axis the co-ordinate will lie on $y$ axis and will be parallel to $x$ axis.

Step 2. Justification for part (b).

Given information $y=0$ is the equation of $x$ axis and the coordinate will lie on $x$ axis  and parallel to $y$ axis.

Step 3. Justification for part (c).

Given information $x+y=0$ stated that every $y$ co-ordinate is negative corresponding to $x$.

Step 4. Justification for part (d).

Given information $xy=0$ is the union of all points which lie in $YOZ$ plane or on $ZOX$ plane.The equation $xy=0$ represents a pair of perpendicular planes.

Step 5. Justification for part (e).

Given information $x^2+y^2=0$ represents an equation of ellipse centered at origin with axes lying along the co-ordinate axes.