If the lines $2 x+3 y+1=0$ and $3 x-y-4=0$ lie along diameters of a circle of circumference $10 \pi$, then the equation of the circle is

(A) $x^{2}+y^{2}-2 x+2 y-23=0$

(B) $x^{2}+y^{2}-2 x-2 y-23=0$

(C) $x^{2}+y^{2}+2 x+2 y-23=0$

(D) $x^{2}+y^{2}+2 x-2 y-23=0$

JEE Main · 2004 · 24 Apr 2004 · Offline · Circle

If the lines

2 x + 3 y + 1 = 0

and

3 x - y - 4 = 0

lie along diameters of a circle of circumference

10 π

, then the equation of the circle is

(A) $x^{2} + y^{2} - 2 x + 2 y - 23 = 0$ ✓ Correct
(B) $x^{2} + y^{2} - 2 x - 2 y - 23 = 0$
(C) $x^{2} + y^{2} + 2 x + 2 y - 23 = 0$
(D) $x^{2} + y^{2} + 2 x - 2 y - 23 = 0$

Answer: (A)

Solution

The centre is where the two diameters meet. Solving

2 x + 3 y + 1 = 0

with

3 x - y - 4 = 0

gives

x = 1

and

y = - 1

, so the centre is

(1, - 1)

. A circumference of

10 π

means

2 π r = 10 π

, so

r = 5

. The circle

(x - 1)^{2} + (y + 1)^{2} = 25

expands to

x^{2} + y^{2} - 2 x + 2 y - 23 = 0

JEE Main · 2004 · 24 Apr 2004 · Offline · 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 →