KVPY SX SB Exam 19-Nov-2017 Question Paper

Question : 1 of 120

Marks: +1, -0

Consider a rigid square ABCD as in the figure with A and B on the x and y axis respectively.

When A and B slide along their respectiveaxes, the locus of C forms a part of

Solution:

C(h, k)

h = a \sin θ⇒\sin θ =h/a

k = a sinθ + a cos θ
k = h + a cos θ

{k-h}/a=\cosθ

....(2)

\sin^2 θ + \cos^2 θ= 1

h^2/a^2+(k-h)^2/a^2=1

h ^2 + (k -h)^2 = a ^2

locus

x^2 + (y -x)^2 = a^2

solving we get

x^2 + y^2 + x^2-2xy = a^2

2x^2 + y^2-2xy = a^2

check

h^2-ab < 0

ellipse

Go to Question:

Next Question