JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Straight Lines

In a triangle

P QR

, the co-ordinates of the points

P

and

Q

are

(- 2, 4)

and

(4, - 2)

respectively. If the equation of the perpendicular bisector of

P R

2 x - y + 2 = 0

, then the centre of the circumcircle of the

△ P QR

is:

(A) $(0, 2)$
(B) $(- 2, - 2)$ ✓ Correct
(C) $(- 1, 0)$
(D) $(1, 4)$

Answer: (B)

Solution

The circumcentre is equidistant from

P

and

Q

, so it lies on the perpendicular bisector of

P Q

. The midpoint of

P Q

(1, 1)

and the slope of

P Q

\frac{- 2 - 4}{4 + 2} = - 1

, so that bisector has slope

1

and equation

y = x

. The circumcentre also lies on the perpendicular bisector of

P R

, which is

2 x - y + 2 = 0

. Substituting

y = x

gives

2 x - x + 2 = 0

, so

x = - 2

and

y = - 2

. The centre of the circumcircle is

(- 2, - 2)

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Straight Lines →

More JEE Main questions on Straight Lines

Let a point A lie between the parallel lines $L_{1}$ and $L_{2}$ such that its distances from $L_{1}$ and $L_{2}$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC , where the points B and C l …
JEE Main 2026View solution →
Among the statements
(S1): If $A (5, - 1)$ and $B (- 2, 3)$ are two vertices of a triangle, whose orthocentre is $(0, 0)$ , then its third vertex is $(- 4, - 7)$ and
(S2): If positive numbers $2 a, b, c$ are three consecutive terms of an A.P., then the lines $a x + b y + c = 0$ are …
JEE Main 2026View solution →
A rectangle is formed by the lines $x = 0$ , $y = 0$ , $x = 3$ and $y = 4$ . Let the line L be perpendicular to $3 x + y + 6 = 0$ and divide the area of the rectangle into two equal parts. Then the distance of the point $(\frac{1}{2}, - 5)$ …
JEE Main 2026View solution →
Let $A (1, 2)$ and $C (- 3, - 6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $7 x - y = 14$ . If $B (α, β)$ and $D (γ, δ)$ are the other two vertices, then …
JEE Main 2026View solution →
Let $A (1, 0), B (2, - 1)$ and $C (\frac{7}{3}, \frac{4}{3})$ be three points. If the equation of the bisector of the angle ABC is $α x + β y = 5$ , then the value of $α^{2} + β^{2}$ is
JEE Main 2026View solution →
Let the angles made with the positive x-axis by two straight lines drawn from the point $P (2, 3)$ and meeting the line $x + y = 6$ at a distance $\frac{2}{3}$ from the point P be $θ_{1}$ and $θ_{2}$ . Then the value of …
JEE Main 2026View solution →