AP EAMCET202318 May 2023Evening ShiftMathematicsStraight LinesActual
The square of the distance from the origin to the point of intersection of the pair of lines a x^2+2 h x y-a y^2+2 g x+2 fy + c =0 is
Options
- Af ^2+ g ^2 a ^2+ h ^2
- Bf ^2+ g ^2 a ^2- h ^2
- Cf ^2+ g ^2 ~h ^2- a ^2
- Df ^2- g ^2 ~h ^2- a ^2
Correct answer
A. f ^2+ g ^2 a ^2+ h ^2
Step-by-step solution
The equation of pair of lines is a x^2+2 h x y-a y^2+2 g x+2 f y+c=0.....(i) Let the lines represented by the given equation be aligned & l x+m y+n=0.....(ii) & l^ x+m^ y+n^ =0.....(iii) aligned from eqs. (i), (ii) & (iii) aligned & a x^2+2 h x y-a y^2+2 g x+2 f y+c=(l x+m y+n) & (l^ x+m^ y+n^ ) aligned Equating the coefficients, we get aligned & ll ^ = a , mm ^ =- a , nn ^ = c & mn ^ + m ^ n =2 f , nl ^ + n ^ l =2 ~g , ~lm ^ + ml ^ =2 ~h aligned Solving eqn. (ii) & (iii) by cross multiplication: x m^ -m^ n = y n^