JEE Main 2022 · 27 Jul · Shift 2 · Mathematics Q11

← JEE Main 2022 · 27 Jul · Shift 2

MathematicsSingle correct+4 / -1Question 11 of 90

The equations of the sides AB, BC and CA of a triangle ABC are $2x+y=0$ , $x+py=39$ and $x-y=3$ respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true ?

(AC)^2=9p

(AC)^2+p^2=136

32<\text{area}(\Delta ABC)<36

34<\text{area}(\Delta ABC)<38

Answer and worked solution

Official answer: D

Vertices. $A=(1,-2)$ . The circumcircle $(x-2)^2+(y-3)^2=26$ gives $B=\left(-\frac{13}5,\frac{26}5\right)$ and $C=(7,4)$ , so $p=8$ .

Check. $AC^2=72=9p$ and $72+64=136$ , so (A) and (B) hold. Area $=32.4$ , so (C) holds and (D) fails.

(D)

Topics:Equations of a line Equation of a circle

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JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 11