Question

The locus of the point x = 2(cost + sint),
y = 5(cost - sint) is​

Answer 1

Answer:

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Answer 2

Answer:

Ellipse

Given, x=2(cost+sint)

⇒

2

x

=cost+sint ...(i)

And y=5(cost−sint)

⇒

5

y

=cost−sint ...(ii)

Then (

2

x

)

2

+(

5

y

)

2

=(cost+sint)

2

+(cost−sint)

2

=cos

2

t+sin

2

t+2cost.sint+cos

2

t+sin

2

t−2cost.sint

=2(cos

2

t+sin

2

t)

=2

Hence, (

2

x

)

2

+(

5

y

)

2

=2

4

x

2

+

25

y

2

=2

8

x

2

+

50

y

2

=1