(D) The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = d$. Given points are $(a, 2)$ an

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

(D) The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = d$. Given points are $(a, 2)$ and $(3, 4)$ with distance $d = 8$. So,$\sqrt{(3 - a)^2 + (4 - 2)^2} = 8$. Squaring both sides,we get $(3 - a)^2 + (2)^2 = 8^2$. $(3 - a)^2 + 4 = 64$. $(3 - a)^2 = 60$. $3 - a = \pm \sqrt{60} = \pm 2\sqrt{15}$. $a = 3 \pm 2\sqrt{15}$.

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

Difficult

If the distance between the points $(a, 2)$ and $(3, 4)$ is $8$,then $a = $

A
$2 + 3\sqrt{15}$
B
$2 - 3\sqrt{15}$
C
$2 \pm 3\sqrt{15}$
D
$3 \pm 2\sqrt{15}$

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

The coordinates of the point of trisection of the line segment joining the points $(-2, 3)$ and $(3, -1)$ that is nearer to $(-2, 3)$ are

Medium

View Solution

Find the distance between the points $P(-2, 3)$ and $Q(4, -1)$.

Easy

View Solution

Three points $P, Q,$ and $R$ lie on the line segment joining points $A(-6, 8)$ and $B(8, -6)$ such that $AP = PQ = QR = RB$. Find the coordinates of $R$.

Medium

View Solution

If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to

EasyAP EAMCET 2004

View Solution

If the line segment joining the points $A(a, b)$ and $B(c, d)$ subtends an angle $\theta$ at the origin,then $\cos \theta$ is equal to

DifficultIIT 1961

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

If the distance between the points $(a, 2)$ and $(3, 4)$ is $8$,then $a = $

Similar Questions

The coordinates of the point of trisection of the line segment joining the points $(-2, 3)$ and $(3, -1)$ that is nearer to $(-2, 3)$ are

Find the distance between the points $P(-2, 3)$ and $Q(4, -1)$.

Three points $P, Q,$ and $R$ lie on the line segment joining points $A(-6, 8)$ and $B(8, -6)$ such that $AP = PQ = QR = RB$. Find the coordinates of $R$.

If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to

If the line segment joining the points $A(a, b)$ and $B(c, d)$ subtends an angle $\theta$ at the origin,then $\cos \theta$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module