CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the tangent at the point P(2,4) to the parabola y2=8x meets the parabola y2=8x+5 at Q and R, then the mid-point of QR is

A
(4,2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(2,4)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(7,9)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(9,7)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is D (2,4)
The equation of the tangent y2=8x at P(2,4) is
4y=4(x+2)
xy+2=0....(i)
Let (x1,y1) be the mid-point of chord QR. Then, equation of QR is
yy14(x+x1)5=y218x15
4xyy14x1+y21=0....(ii)
Clearly, Eqs. (i) and (ii) represent the same line
41=y11=4x1+y212
y1=4;8=4x1+y1
y1=4;x1=2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
General and Particular Solutions of a DE
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon