Question

Find the equation of the tangent to the ellipse
2x2 + y2 = 8 which are :
i) parallel to x - 2y - 4 = 0
ii) perpendiuclar to x + y + 2 = 0.​

Answer 1

Answer:

ANSWER

Equaton of ellipse-

2x2+y2=8

⇒4x2+8y2=1

Here,

a2=4

b2=8

Given equation of tangent-

x−2y−4=0

y=2x−24

Now,

(i) Equation of tangent parallel to y=2x−24 is-

y=2x+2k.....(1)

Here

m=21

c=2k

Equation (1) is tangent to the ellipse if

c2=a2m2+b2

(2k)2=4×41