Straight Lines JEE Main PYQs, 2020 to 2025

Let ABC be the triangle such that the equations of lines AB and AC be $3y-x=2$ and $x+y=2$, respectively, and the points B and C lie on $x$-axis. If P is the orthocentre of the triangle ABC , then the area of the triangle PBC is equal to

Let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $\left(k, \frac{k}{2}\right)$ from the line $3 x+4 y+5=0$ is

If A and B are the points of intersection of the circle $x^{2}+y^{2}-8x=0$ and the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$ and a point P moves on the line $2x-3y+4=0$, then the centroid of $\Delta PAB$ lies on the line :

If the line segment joining the points $(5,2)$ and $(2,a)$ subtends an angle $\frac{\pi}{4}$ at the origin, then the absolute value of the product of all possible values of $a$ is :