wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The normal at (4,4) to the parabola y2=4x is given by L=0. If S:x236+y2201=0 be an ellipse, then

A
L=0 passes through a focus of the ellipse.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
L=0 passes through a vertex of the ellipse.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
L=0 parallel to the major axis of the ellipse.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
L=0 parallel to the minor axis of the ellipse.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B L=0 passes through a vertex of the ellipse.
Given parabola : y2=4x
Point (4,4)= (at2,2at)
t=2 ( a=1)
Equation of normal at t is
y+xt=2at+at3y+2x=122x+y12=0

Now, the equation of ellipse is
x236+y220=1
Here,
a2=36, b2=20e2=1b2a2e=12036=23
Foci =(±ae,0)=(±4,0)
Verticec =(±6,0)
So, L=0 passes through the vertex (6,0)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon