Tangents are drawn from origin to the curve `y = sin+cos x`·Then their points of contact lie on the curve

Options

A. `(1)/(x^(2))+(2)/(y^(2))=1`
B. `(2)/(x^(2))-(1)/(y^(2))=1`
C. `(2)/(x^(2))+(1)/(y^(2))=1`
D. `(2)/(y^(2))-(1)/(x^(2))=1`

Answer

D

Explanation

`y_(1)=sqrt2sin(x_(1)+(pi)/(4)),(dy)/(dx)=(y_(1))/(x_(1))` where `(x_(1),y_(1))` is point on the curve
`therefore" "(y_(1)^(2))/(x_(1)^(2))=2cos^(2)(x_(1)+(pi)/(4))=2((-y_(1)^(2))/(2)+1)`
`rArr" Locus of "(x_(1)y_(1))" is "(2)/(y^(2))-(1)/(x^(2))=1`