
What is the locus of first degree equation in \[x,y,z\]?
A. Straight line
B. Plane
C. Sphere
D. Curved surface
Answer
164.1k+ views
Hint: As in this question, locus point of an equation is given and apart from that, no further information is provided. So, to solve this type of question, we will take options to find out the answer. Here, we will compare the equation which will be formed by every option and compare with the said equation and whichever equation fits the criteria will be the correct option.
Formula Used:
1. Equation of straight line:
$\dfrac{{x - a}}{\alpha } = \dfrac{{y - b}}{\beta } = \dfrac{{z - c}}{\gamma }$
2. Equation of plane:
$\alpha x + \beta b + \gamma y = \delta $
3. Equation of sphere:
${(x - a)^2} + {(y - b)^2} + {(z - c)^2} = {r^2}$
Complete Step-by-step solution
Let us assume the equation as $ax + by + cz = d$
Now, we will compare the assumed equation with each equation formed by the given options.
Checking the equation of option A:
The equation of straight line is
$\dfrac{{x - a}}{\alpha } = \dfrac{{y - b}}{\beta } = \dfrac{{z - c}}{\gamma }$
The above equation does not match with the assumed equation.
So, option A is incorrect.
Checking the condition of option B:
The equation of plane is
$\alpha x + \beta b + \gamma y = \delta $
The above equation matches with the assumed equation.
So, option B is correct.
Checking the condition of option C:
The equation of sphere is
${(x - a)^2} + {(y - b)^2} + {(z - c)^2} = {r^2}$
The above equation does not match with the assumed equation.
So, option C is incorrect.
Checking the condition of option D:
The equations for curved surface can’t be delivered easily as it depends on the surface.
So, option D is also incorrect.
Hence the correct option is B.
Note:A locus is a collection of points that satisfy a particular requirement or circumstance for a shape or figure. For this type of question, it is important to know the equations of different shapes in all forms.
Formula Used:
1. Equation of straight line:
$\dfrac{{x - a}}{\alpha } = \dfrac{{y - b}}{\beta } = \dfrac{{z - c}}{\gamma }$
2. Equation of plane:
$\alpha x + \beta b + \gamma y = \delta $
3. Equation of sphere:
${(x - a)^2} + {(y - b)^2} + {(z - c)^2} = {r^2}$
Complete Step-by-step solution
Let us assume the equation as $ax + by + cz = d$
Now, we will compare the assumed equation with each equation formed by the given options.
Checking the equation of option A:
The equation of straight line is
$\dfrac{{x - a}}{\alpha } = \dfrac{{y - b}}{\beta } = \dfrac{{z - c}}{\gamma }$
The above equation does not match with the assumed equation.
So, option A is incorrect.
Checking the condition of option B:
The equation of plane is
$\alpha x + \beta b + \gamma y = \delta $
The above equation matches with the assumed equation.
So, option B is correct.
Checking the condition of option C:
The equation of sphere is
${(x - a)^2} + {(y - b)^2} + {(z - c)^2} = {r^2}$
The above equation does not match with the assumed equation.
So, option C is incorrect.
Checking the condition of option D:
The equations for curved surface can’t be delivered easily as it depends on the surface.
So, option D is also incorrect.
Hence the correct option is B.
Note:A locus is a collection of points that satisfy a particular requirement or circumstance for a shape or figure. For this type of question, it is important to know the equations of different shapes in all forms.
Recently Updated Pages
Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

Trending doubts
Degree of Dissociation and Its Formula With Solved Example for JEE

Instantaneous Velocity - Formula based Examples for JEE

JEE Main Chemistry Question Paper with Answer Keys and Solutions

JEE Main Reservation Criteria 2025: SC, ST, EWS, and PwD Candidates

JEE Mains 2025 Cut-Off GFIT: Check All Rounds Cutoff Ranks

Lami's Theorem

Other Pages
Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates

Neet Cut Off 2025 for MBBS in Tamilnadu: AIQ & State Quota Analysis

Karnataka NEET Cut off 2025 - Category Wise Cut Off Marks

NEET Marks vs Rank 2024|How to Calculate?

NEET 2025: All Major Changes in Application Process, Pattern and More
