Question

The question is in the photo, that answer is not correct. At least I do not know if it is.

Answer 1

Explanation:

To get the solution lying in the shaded region,

Justify the equation with the given options,

Option (1)

`(x^2)/(16)+(y^2)/(4)\leq 1`

For (1, 1),

`(1^2)/(16)+(1^2)/(4)\leq 1`

`(1)/(16)+(1)/(4)\leq 1`

`(1+4)/(16)\leq 1`

`(5)/(16)\leq 1`

True.

Therefore, point (1, 1) justifies the equation.

Option (2)

For (4, 1),

`(x^2)/(16)+(y^2)/(4)\leq 1`

`(4^2)/(16)+(1^2)/(4)\leq 1`

`1+(1)/(4)\leq 1`

`1(1)/(4)\leq 1`

False.

Therefore, point (4, 1) doesn't justify the equation.

Option (3)

For (-1, 2),

`(x^2)/(16)+(y^2)/(4)\leq 1`

`((-1)^2)/(16)+((2)^2)/(4)\leq 1`

`(1)/(16)+1\leq 1`

`1(1)/(16)\leq 1`

False.

Therefore, point (-1, 2) doesn't justify the equation.

Option (4)

For (2, -2),

`(x^2)/(16)+(y^2)/(4)\leq 1`

`(2^2)/(16)+((-2)^2)/(4)\leq 1`

`(1)/(4)+1\leq 1`

`1(1)/(4)\leq 1`

False.

Therefore, point (2, -2) doesn't justify the equation.

Option (1) will be the answer.