wiz-icon
MyQuestionIcon
MyQuestionIcon
7
You visited us 7 times! Enjoying our articles? Unlock Full Access!
Question

If the chord of contact of the tangents from a point P to the parabola y2=4ax touches the parabola x2=4by, then the locus of P is

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

The correct option is A xy=2ab
Let P(h,k)
Equation of chord of contact for parabola y2=4ax is
yk=2a(x+h)
y=2axk+2ahk (1)
Equation of tangent for x2=4by will be of form y=mxbm2 (2)

As equation (1) and (2) represent the same line, so,
m=2ak and
2ahk=bm2
2ahk=b(2ak)2
hk=2ab
Hence, the locus of the point P will be xy=2ab

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon