Analytical Geometry Pn Chatterjee Pdf Link ● (EXCLUSIVE)

| Geometry | Standard Form | Key Parameters | Useful Derived Formula | |----------|---------------|----------------|------------------------| | | (ax + by + c = 0) | slope = (-a/b) (if (b \neq 0)) | Distance from ((x_1,y_1)) to line: (\displaystyle \fracax_1+by_1+c\sqrta^2+b^2) | | Circle | ((x-h)^2+(y-k)^2=r^2) | centre ((h,k)), radius (r) | Power of a point (P): (PO^2 - r^2) | | Parabola (axis along x) | ((y-k)^2 = 4a(x-h)) | focus ((h+a, k)) | Latus‑rectum = (4a) | | Ellipse | (\displaystyle \frac(x-h)^2a^2+\frac(y-k)^2b^2=1) ( (a>b) ) | eccentricity (e = \sqrt1-b^2/a^2) | Distance between foci = (2ae) | | Hyperbola (horizontal) | (\displaystyle \frac(x-h)^2a^2-\frac(y-k)^2b^2=1) | eccentricity (e = \sqrt1+b^2/a^2) | Asymptotes: (y-k = \pm \fracba(x-h)) | | General 2nd‑degree | (Ax^2+2Hxy+By^2+2Gx+2Fy+C=0) | Discriminant (\Delta = ABC + 2FGH - AF^2 - BG^2 - CH^2) | (\Delta>0) ⇒ ellipse/hyperbola; (\Delta=0) ⇒ parabola | | Plane (3‑D) | (ax+by+cz+d=0) | normal vector ((a,b,c)) | Distance from ((x_0,y_0,z_0)): (\displaystyle \frac\sqrta^2+b^2+c^2) | | Line (3‑D) | (\fracx-x_1l=\fracy-y_1m=\fracz-z_1n) | direction ratios ((l,m,n)) | Shortest distance between two skew lines: (\displaystyle \frac(\mathbfr_2-\mathbfr_1)\cdot (\mathbfd_1\times\mathbfd_2)) |

: Direction cosines, planes, spheres, cones, cylinders, and conicoids. Problem Sets analytical geometry pn chatterjee pdf link