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

The normal to the curve x2=4y passing (1,2) is

A
x+y=3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
xy=3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x+y=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
xy=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
E
answer required
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is E x+y=3
Given, x2=4y
Slope of tangent to the curve will be 4dydx=2x
dydx=x2
So slope of normal will be dxdy=2x
Let the point on the curve be (h,k)
So slope of normal will be 2h
Equation of normal is given by (yk)=2h(xh)
It is given that the normal passes through (1,2)
(2k)=2h(1h).............(1)
Also, (h,k) lies on the curve so h2=4k
From (1) we have
h34=2h+22h=2
h3=8
h=2
k=h24k=1
So the equation will be
y1=22(x2)
x+y=3

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometrical Interpretation of a Derivative
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon