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

Let P be a variable point. From P,PQ and PR are tangents drawn to the parabola y2=4x. If QPR is always 45, then the locus of P is

A
x2y2+6x+1=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x2+y2+6x+1=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x2y26x+1=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x2+y26x+1=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A x2y2+6x+1=0

y=mx+1m is equation of tangent to a parabola y2=4x with slope m.

m2xmy+1=0

If m1 and m2 are roots of this equation then

m1+m2=yx;m1m2=1x

m1m2=±(yx)24(1x)=±y24xx

tan450=1=±m1m21+m1m2

1+1x=±y24xx

x2+1+2x=y24x

x2+1+6xy2=0

Hence, option 'A' is correct.


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