wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let OABC be a rectangle, where O is the origin and A, C lie on the parabola y=x2. If B lies on a parabola whose vertex coordinates is (α,β), then the value of α+β is

A
2.0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
2.00
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution


Let the coordinates of A be (t,t2)
and coordinates of C be (a,a2).
OAOC
mOA×mOC=1t20t0×a20a0=1a=1t
Coordinates of C is (1t,1t2)

Let coordinates of B be (h,k).
Since, the diagonals OB and AC bisect each other, we have
(h2,k2)=⎜ ⎜ ⎜t1t2,t2+1t22⎟ ⎟ ⎟
h=t1t, k=t2+1t2

Now, h2=t2+1t22
h2=k2
Locus of point B is y=x2+2
Vertex of the parabola is (α,β)=(0,2)
α+β=2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Comparisons between different quadrilaterals
Watch in App
Join BYJU'S Learning Program
CrossIcon