Question

What is the locus of a point for which $y=0,z=0$?
A. x-axis
B. y-axis
C. z-axis
D. yz-plane

Answer 1

Hint: In order to find the locus of a curve first of all define the term locus. then find the relation which exists between the coordinates of any point on the curve. One we find the relation we can write the equation of the locus of the curve. In this question define the position of any point with respect to x, y and z axis respectively, then find the condition for which $y=0,z=0$ is satisfied. This condition is the desired locus.

Complete step-by-step answer:
LOCUS: when a point moves so as to satisfy a given condition, or conditions, the path it traced out is its locus under these conditions.
Let us draw the position of a point with respect to x, y and z axis respectively. Suppose p (x ,y, z) be the point.

                             

As we know that
X- coordinate of a point is the distance from the y and z axis respectively.

Y- coordinate of a point is the distance from x and z axis respectively.

Z- coordinate of a point is the distance from the y and x axis respectively.

As from the question we have to find the locus of a point whose distance from y-axis and z -axis is zero.
So, any point which satisfies the above conditions must lie on X-axis as the distance of any point on X-axis is zero from y-axis as well as z-axis.
Hence option A is correct.


Note: It should be noted here that we find the desired locus in the Rectangular system in which all the three axes are perpendicular to each other. The point of intersection of all three axes is origin. This system is also known as an orthogonal coordinate system.