Manipal MET2020MathematicsEllipse
The condition for the line l x+m y+n=0 to be a normal to x^2 25 + y^2 9 =1 is
Options
- Al^2 9 + m^2 25 = n^2 256
- B9 m^2 + 25 l^2 = 256 n^2
- Cl^2 9 - m^2 25 = n^2 256
- DNone of these
Correct answer
B. 9 m^2 + 25 l^2 = 256 n^2
Step-by-step solution
Given equation of line is l x+m y+n=0 and equation of ellipse is x^2 25 + y^2 9 =1 . The equation of any normal to the ellipse is 5 x -3 y cosec =25-9 5 x -3 y cosec -16=0 As the Eq. (i) is the normal to the ellipse. 5 l = -3 cosec m = -16 n = 5 n -16 l and = 3 n 16 m ^2 + ^2 =1 ( 5 n 16 l )^2+ ( 3 n 16 m )^2=1 25 n^2 256 l^2 + 9 n^2 256 m^2 =1 25 l^2 + 9 m^2 = 256 n^2