Ellipse

Any point on the ellipse is

(%5Csqrt%7B14%7D%20cos%5C%2C%5Ctheta%2C%20%5Csqrt%7B5%7D%20sin%5C%2C%5Ctheta)

%5Ctherefore

Equation of normal at

(%5Csqrt%7B14%7D%5C%2Ccos%5C%2C%5Ctheta%2C%20%5Csqrt%7B5%7D%5C%2Csin%5C%2C%5Ctheta)

%5Csqrt%7B14%7D%20x%5C%2Csec%5C%2C%5Ctheta%2C%20%5Csqrt%7B5%7Dy%5C%2Ccosec%5C%2C%5Ctheta%20%3D%209

Since, it passes through

(%5Csqrt%7B14%7D%20%5C%2Ccos%5C%2C2%5Ctheta%2C%20%5Csqrt%7B5%7D%5C%2Csin%5C%2C2%5Ctheta)

%5Ctherefore%20%5Csqrt%7B14%7D%5Csqrt%7B14%7D%20%5C%2Ccos%5C%2C2%5Ctheta%20%5C%2Csec%5C%2C%5Ctheta

-%20%5Csqrt%7B5%7D%20%5Csqrt%7B5%7D%5C%2Csin%5C%2C2%5Ctheta%20%5C%2Ccosec%5C%2C%5Ctheta%20%3D%209

%5CRightarrow%2014%20%5Cfrac%7Bcos%5C%2C2%5Ctheta%7D%7Bcos%5C%2C%5Ctheta%7D%20-%205%20%5Cfrac%7Bsin%5C%2C%5Ctheta%7D%7Bsin%5C%2C%5Ctheta%7D%20%3D%209

%5CRightarrow%2014(2%5C%2Ccos%5E2%5C%2C%5Ctheta%20-1)%20-%2010%5C%2Ccos%5E2%5C%2C%5Ctheta%20%3D%209%5C%2Ccos%5C%2C%5Ctheta

%5CRightarrow%2018%5C%2Ccos%5E2%5Ctheta%20-%209%5C%2Ccos%5C%2C%5Ctheta%20-%2014%20%3D%200

%5CRightarrow%20(3%5C%2Ccos%5C%2C%5Ctheta%20%2B%202)(6%5C%2Ccos%5C%2C%5Ctheta%20-%207)%20%3D%200

%5CRightarrow%20cos%5C%2C%5Ctheta%20%3D%20-%5Cfrac%7B2%7D%7B3%7D%2C%20cos%5C%2C%5Ctheta%20%5Cne%20%5Cfrac%7B7%7D%7B6%7D

Chapter Questions
1 MCQs