Let C be a circle with radius units and centre at the origin. Let the line x + y = 2 intersects the circle C at the points P and Q. Let MN be a chord of C of length 2 units and slope –1. Then a distance (in units) between the chord PQ and the chord MN is

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Let C be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line x + y = 2 intersects the circle C at the points P and Q. Let MN be a chord of C of length 2 units and slope –1. Then a distance (in units) between the chord PQ and the chord MN is [2024]

1 $3 - \sqrt{2}$

2 $2 - \sqrt{3}$

3 $\sqrt{2} + 1$

4 $\sqrt{2} - 1$

Ans.
(1)

Distance of centre from chord $P Q =$ $| \frac{0 + 0 - 2}{\sqrt{1^{2} + 1^{2}}} |$ $= \frac{2}{\sqrt{2}} = \sqrt{2}$

Let distance of centre from chord MN = p, then length of chord = $2 \sqrt{10 - p^{2}}$

$\Rightarrow 2 \sqrt{10 - p^{2}} = 2$ ( $∵$ Given)

$\Rightarrow 10 - p^{2} = 1 \Rightarrow p^{2} = 9 \Rightarrow p = 3$

$\Rightarrow$ Distance between chord PQ and MN = $3 - \sqrt{2}$ .

Want Us to Email you About Special Offers & Updates?