Question

The eccentric angle of the point where the line, 5x – 3y = 8/2 is a normal to the ellipse
25
x?
= l is
공
Зл
(
A)
3
TT
4
(B)
TC
4
(c)
(D) tan-2
ago​

Answer 1

Answer:

The equation of the normal to the ellipse

a

2

x

2

+

b

2

y

2

=1 at the point P(acosθ,bsinθ) is axsecθ−bycosecθ=a

2

−b

2

Given,ellipse equation as

5

2

x

2

+

3

2

y

2

=1

⇒ Length of major axis, a=5 and length of minor axis, b=3.

∴The required equation of normal is 5xsecθ−3ycosecθ=5

2

−3

2

⇒5xsecθ−3ycosecθ=16…(1)

Given normal equation 5x−3y=8

2

Multiplying both sides with

2

⇒5

2

x−3

2

y=16…(2)

Comparing equation (1) and (2)

⇒secθ=

2

⇒cosθ=

2

1

⇒θ=

4

π