CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let P,Q,R be the points on the auxiliary circle of ellipse x2a2+y2b2=1(a>b) , such that PQR is an equilateral triangle and PQR is corresponding triangle inscribed within the ellipse. Then centroid of the triangle PQR lies at 


A
centre of the ellipse
loader
B
focus of the ellipse 
loader
C
between focus and centre of the ellipse
loader
D
between one extremity of minor axis and centre of the ellipse
loader

Solution

The correct option is A centre of the ellipse
Let points on equilateral triangle be triangleP(θ),Q(θ+2π3),R(θ+4π3)
then
P(acosθ,bsinθ)Q(acos(θ+2π3),bsin(θ+2π3))R(acos(θ+4π3),bsin(θ+4π3))

Let centroid of PQR(x,y)
x=a⎢ ⎢ ⎢ ⎢cos(θ)+cos(θ+2π3)+cos(θ+4π3)3⎥ ⎥ ⎥ ⎥x=a3[cosθ+2cos(θ+π)cosπ3]=0

And 
y=b⎢ ⎢ ⎢ ⎢sin(θ)+sin(θ+2π3)+sin(θ+4π3)3⎥ ⎥ ⎥ ⎥y=b3[sinθ+2sin(θ+π)cosπ3]=0

Hence centroid is (0,0), which is the centre of the ellipse.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image