JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Circle

Let

C

be a circle with radius

10

units and centre at the origin. Let the line

x + y = 2

intersect the circle

C

at the points

P

and

Q

. Let

M N

be a chord of

C

of length 2 units and slope

- 1

. Then, the distance (in units) between the chord

P Q

and the chord

M N

(A) $3 - 2$ ✓ Correct
(B) $2 - 1$
(C) $2 - 3$
(D) $2 + 1$

Answer: (A)

Solution

Circle

C : x^{2} + y^{2} = 10

, radius

10

. Chord

M N

has length 2, so its half-length is 1; the perpendicular distance from the centre O to

M N

10 - 1 = 3

.

Line

P Q : x + y = 2

is at perpendicular distance

\frac{∣0 + 0 - 2∣}{2} = 2

from O.

M N

has slope

- 1

, parallel to

P Q

(also slope

- 1

). Placing

M N

on the same side as

P Q

, the distance between the two parallel chords is

∣3 - 2 ∣ = 3 - 2

JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Circle →

More JEE Main questions on Circle

Let PQ and MN be two straight lines touching the circle $x^{2} + y^{2} - 4 x - 6 y - 3 = 0$ at the points A and B respectively. Let O be the centre of the circle and $∠ AOB = π /3$ . Then the locus of the point of intersection of the lines PQ and MN is:
JEE Main 2026View solution →
If P is a point on the circle $x^{2} + y^{2} = 4$ , Q is a point on the straight line $5 x + y + 2 = 0$ and $x - y + 1 = 0$ is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such point P is ______.
JEE Main 2026View solution →
Let the set of all values of r, for which the circles $(x + 1)^{2} + (y + 4)^{2} = r^{2}$ and $x^{2} + y^{2} - 4 x - 2 y - 4 = 0$ intersect at two distinct points be the interval ( $α$ , $β$ ). Then $α β$ is equal to
JEE Main 2026View solution →
Let a circle of radius 4 pass through the origin O , the points $A (- 3 a, 0)$ and $B (0, - 2 b)$ , where a and b are real parameters and $ab \neq = 0$ . Then the locus of the centroid of $△ OAB$ is a cir …
JEE Main 2026View solution →
Let $y = x$ be the equation of a chord of the circle $C_{1}$ (in the closed half-plane $x \geq 0$ ) of diameter 10 passing through the origin. Let $C_{2}$ be another circle described on the given chord as its diameter. If the equation of the chord …
JEE Main 2026View solution →
Let the circle $x^{2} + y^{2} = 4$ intersect $x$ -axis at the points $A (a, 0), a > 0$ and $B (b, 0)$ . Let $P (2 cos α, 2 sin α), 0 < α < \frac{π}{2}$ and $Q (2 cos β, 2 sin β)$ be two points …
JEE Main 2026View solution →