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

If the tangents at any point P on the ellipse x2a2+y2b2=1 meets the tangents at the vertices A and A in L and L respectively, then AL.AL=

A
a+b
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a2+b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
b2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D b2

Let tangent is drawn at any point P(acosθ,bsinθ) on the ellipse x2a2+y2b2=1 then equation of tangent is

xacosθ+ybsinθ=1......(i)

Equation of tangent at A(a,0) is x=a

Put x=a in (i)

aacosθ+ybsinθ=1y=(1cosθ)bsinθAL=(1cosθ)bsinθ

Equation of tangent at A(a,0) is x=a

Put x=a in (i)

aacosθ+ybsinθ=1y=(1+cosθ)bsinθAL=(1+cosθ)bsinθ

AL.AL=((1cosθ)bsinθ)((1+cosθ)bsinθ)AL.AL=(1cos2θ)b2sin2θAL.AL=b2

Hence, option D is correct.


701165_551588_ans_702a22e78e0c4dacaca5d7c80bd5ffc1.png

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