Quant · Geometry

Coordinate Geometry

3 sub-topics · 42 lessons · 80 questions · 24 PYQs

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Straight Lines18 lessons · 33 questions · 7 PYQs

Circles in the Plane15 lessons · 25 questions · 10 PYQs

Regions, Areas and Loci9 lessons · 22 questions · 7 PYQs

Formula sheet

Circle on a given diameter
$(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$
Distance between two points
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Lattice points in a diamond
$\#\{|x|+|y|\le n\}=2n^2+2n+1,\quad \#\{|x|+|y|=n\}=4n$
Angle between the two tangents from a point
$\tan\frac{\theta}{2}=\frac{r}{L},\quad \tan\theta=\frac{2rL}{L^2-r^2}$
Area of a triangle from its vertices
$\text{Area}=\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|$
Centre and radius from the general equation
$x^2+y^2+2gx+2fy+c=0:\ \text{centre }(-g,-f),\ r=\sqrt{g^2+f^2-c}$
Centroid, incentre and the Euler line
$G=\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right),\quad I=\frac{aA+bB+cC}{a+b+c},\quad G=\frac{H+2O}{3}$
Slope and the forms of a line
$m=\frac{y_2-y_1}{x_2-x_1}=-\frac{a}{b}\ \text{for}\ ax+by+c=0;\quad y-y_1=m(x-x_1);\quad \frac{x}{a}+\frac{y}{b}=1$