(C) Let the point on the $x$-axis be $P(x, 0)$.Given the distance between $P(x, 0)$ and $(2, 3)$ is $c$.Using the distance formula: $\sqrt{(x-2)^2 + (

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) Let the point on the $x$-axis be $P(x, 0)$.Given the distance between $P(x, 0)$ and $(2, 3)$ is $c$.Using the distance formula: $\sqrt{(x-2)^2 + (0-3)^2} = c$.Squaring both sides: $(x-2)^2 + 9 = c^2$.Since $c Therefore,$(x-2)^2 = c^2 - 9$.Since $c^2 Since the square of a real number cannot be negative,there is no real value of $x$ that satisfies this equation.Thus,the number of such points is $0$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

Easy

Find the number of points on the $x$-axis that are at a distance of $c$ units from $(2, 3)$,where $c < 3$.

A
$1$
B
$2$
C
$0$
D
$3$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Line

Subtopic

System of co-ordinates, Distance between two points, Section formulae

In what ratio does the $x$-axis divide the line segment joining the points $(3, -4)$ and $(-5, 6)$?

Easy

View Solution

Three vertices of a parallelogram taken in order are $(-1, -6)$,$(2, -5)$ and $(7, 2)$. The fourth vertex is

Easy

View Solution

The line segment joining the points $(2, -3)$ and $(-5, 6)$ is divided by the $y$-axis in the ratio:

Difficult

View Solution

If the line $2x - 3y + 4 = 0$ divides the line segment joining the points $A(-2, 3)$ and $B(3, -2)$ in the ratio $m:n$,then the point which divides $AB$ in the ratio $-4m:3n$ is

EasyTS EAMCET 2022

View Solution

Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Find the number of points on the $x$-axis that are at a distance of $c$ units from $(2, 3)$,where $c < 3$.

Similar Questions

In what ratio does the $x$-axis divide the line segment joining the points $(3, -4)$ and $(-5, 6)$?

Three vertices of a parallelogram taken in order are $(-1, -6)$,$(2, -5)$ and $(7, 2)$. The fourth vertex is

The line segment joining the points $(2, -3)$ and $(-5, 6)$ is divided by the $y$-axis in the ratio:

If the line $2x - 3y + 4 = 0$ divides the line segment joining the points $A(-2, 3)$ and $B(3, -2)$ in the ratio $m:n$,then the point which divides $AB$ in the ratio $-4m:3n$ is

Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module