Question

Find the locus of the point represented by x=1+cost,y=2+3sint ?

Answer 1

Answer:

9(x−1)

2

+16(y−2)

2

=144

Step-by-step explanation:

x=1+4cosθ and y=2+3sinθ

Hence

4

x−1

=cosθ and

3

y−2

=sinθ.

Therefore

cos

2

θ+sin

2

θ=1

Or

(

4

x−1

)

2

+(

3

y−2

)

2

=1

16

(x−1)

2

+

9

(y−2)

2

=1

144

9(x−1)

2

+16(y−2)

2

=1

Or

9(x−1)

2

+16(y−2)

2

=144.