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

Intersection point of tangent at ends of latus rectum of parabola y2=4x is

A
(1,0)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(1,0)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(0,1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(0,1)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is C (0,1)
The given equation of the parabola is y2=4x
4ax=4xa=1
Equation of latus rectum is x=1
Putting x=1 in equation of parabola
we get
y2=4y=±2
Hence end point of latus rectum are (1,2),(1,2)
Now equation of parabola is
y2=4x
Differentiating on both sides with respect tox
$2y\cfrac{dy}{dx}=4\\ \Rightarrow\cfrac{dy}{dx}
=m=\cfrac{4}{2y}$
At y=2m=1
At y=2am=1
The equation of tangent is given by
(yy1)=m(xx1)
At (1,2)
y2=1(x1)y=x+1
At (1,2)y+2=1(x1)y=x1
Intersection point of two tangent will be
x1=x+12x=2x=1
Now, y=x1y=11y=0
Hence, intersection point (1,0) lies on direction x=1

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Wildlife Conservation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon