Question

The locus of the point x = sin e + cose, y = sin . cose is
a) x² + y² = 1
b) x² = 1 + 2y
c) xy =1
d) 2√xy = 1

plss ans with solutions

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Answer 1

Answer:

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Step-by-step explanation:

Let the mid point be S(h,k)

∴P(2h,0) and Q(0,2k)

equation of PQ:

2h

x

+

2k

y

=1

∵ PQ is tangent to circle at R(say)

∴ OR=1⇒

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

(

2h

1

)

2

+(

2k

1

)

2

−1

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

=1

⇒

4h

2

1

+

4k

2

1

=1

⇒x

2

+y

2

−4x

2

y

2

=0

Aliter:

tangent to circle

xcosθ+ysinθ=1

P:(secθ,0)

Q:(0,cosecθ)

2h=secθ⇒cosθ=

2h

1

& sinθ=

2k

1

(2x)

2

1

+

(2y)

2

1

=1.