Area of Triangle in Coordinate Geometry - Practice Questions & MCQ

Let a line $y=mx(m>0)$ intersect the parabola, $y^2=x_{\text{at a point }\mathrm{P}\text{, other than the }}$ origin. Let the tangent to it at P meet the x-axis at the point Q . If area $(\mathrm{△}OPQ)=4$ sq.units, then m is equal to $$

Drawn from the origin are two mutually perpendicular lines forming an isosceles triangle together with a straight line , then the area of this triangle is:

Let three vectors $\overrightarrow{\mathrm{a}}=\alpha \hat{\mathrm{i}}+4\hat{\mathrm{j}}+2\hat{\mathrm{k}}$, $\overrightarrow{b}=5\hat{i}+3\hat{j}+4\hat{k},\overrightarrow{c}=x\hat{i}+y\hat{j}+z\hat{k}$ from a triangle such that $\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}$ and the area of the triangle is $5\sqrt{6}$. if $\alpha$ is a positive real number, then $|\overrightarrow{\mathrm{c}}{|}^2$ is :

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0,0)$, $(0,41)$ and $(41,0)$ is :

Let $A=(4,0),B=(0,12)$ be two points in the plane. The locus of a point $C$ such that the area of triangle $ABC18\mathrm{sq}$. units are

Let the parabola $y=x^2+\mathrm{px}-3$, meet the coordinate axes at the points $\mathrm{P},\mathrm{Q}$ and R . If the circle C with centre at $(-1,-1)$ passes through the points $P,Q$ and $R$, then the area of $\mathrm{△}PQR$ is :