The equations of the tangents to the ellipse x2+16y2=16, each one of which makes an angle of 60∘ with the x−axis, is
A
y=√3x±1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
y=√3x±3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
y=√3x±5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
y=√3x±7
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is Dy=√3x±7 We have, x2+16y2=16 ⇒x242+y212=1 This is of the form x2a2+y2b2=1, where a2=16 and b2=1 So, the equation of the tangents with slope m are y=mx±√a2m2+b2⋯(1) Given, m=tan60∘ ⇒m=√3 From equation (1), we get y=√3x±√16×3+1 ⇒y=√3x±7