Question

# A square with each side equal to a lies above the x-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle α(0<α<π4) with the positive direction of the x-axis. Equation of a diagonal of the square is

A

y(cos αsin α)=x(sin α+cos α)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

y(sin α+cos α)+x(cos αsin α)=a

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

x(cos αsin α)=y(cos α+sin α)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

x(cos αsin α)y(cos α+sin α)=a

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct options are A y(cos α−sin α)=x(sin α+cos α) B y(sin α+cos α)+x(cos α−sin α)=a Let the side OA make an angle α with the x-axis. Then the coordinates of A are (a cos α, a sin α). Also, the diagonal OB makes an angle α+π4 with the x-axis, so that its equation is y=tan(α+π4)x or y(cos α−sin α)=x(sin α+cos α) Since AC is perpendicular to OB, its slope is −cot (α+π4), and as it passes through A(a cos α, a sin α), its equation is y−a sin α=−cot(π4+α)(x−a cos α) or y(sin α+cos α)+x(cos α−sin α)=a

Suggest Corrections
0
Related Videos
Basic Concepts
MATHEMATICS
Watch in App
Explore more