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

# If tangents drawn to the ellipse at the parametric point θ, where tanθ=2 meets the auxillary circle at P and Q and PQ subtends rightangle at the centre of the ellipse, then eccentricity of the ellipse is

A
35
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
35
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
53
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
23
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C √53Let the equation of the ellipse is x2a2+y2b2=1, a>b So any point on the ellipse will be (acosθ,bsinθ) but tanθ=2⇒sinθ=2√5,cosθ=1√5 Hence equation of tangent will be x√5a+2y√5b=1⋯(1) Now equation of auxillary circle will be x2+y2=a2 homogenizing with (1) we get x2+y2=a2(x√5a+2y√5b)2⇒45x2+y2(1−4a25b2)−4axy5b=0 This will represent ⊥ lines if 45+1−4a25b2=0⇒b2a2=49 Hence e=√1−49=√53

Suggest Corrections
7
Join BYJU'S Learning Program
Join BYJU'S Learning Program