JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q28

← JEE Main 2022 · 26 Jul · Shift 1

MathematicsInteger+4 / -1Question 28 of 90

The equations of the sides AB, BC and CA of a triangle ABC are $2x+y=0$ , $x+py=15a$ and $x-y=3$ respectively. If its orthocentre is $(2,a)$ , $-\dfrac12<a<2$ , then p is equal to ______.

Your answer

Answer and worked solution

Official answer: 3

Vertices. $A=(1,-2)$ from AB and CA. B lies on $2x+y=0$ and C on $x-y=3$ , both on $x+py=15a$ .

Orthocentre conditions $AH\perp BC$ and $BH\perp CA$ give $p=2,\ a=-0.2$ or $p=3,\ a=1$ . Only $a=1$ lies in $\left(-\frac12,2\right)$ , so $p=3$ .

Answer: 3

Topics:Equations of a line Angle between lines

← Previous question Next question →

JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 28