well i have posted some good shrtcts...but many of u havent seen them...

 

so here m posting (pasting them 1ce more)

 

shrtct to find eqn of tangent to ellipse

eg. take this

Q)find the eqn of ellipse if its eqn  of chord is 2x² + 5y² = 20 which is bisected at (2,1) ??????????

Sol....first write eqn in terms of xx₁ and yy₁

like 2xx₁ + 5yy₁ = 20

 

now satisfy this pt. (2,1) here

it will bcome 4x + 5y = 20 now subtract coeff. of x and y (given in very first eqn) frm the rt. hand side's const. term

 

final ans is 4x + 5y = 13