Question

Determine whether the statement is true or false.

The circle (x+4)^2=85 passes through the point (2,-5).
The statement is_____

Answer 1

statement is true!

Explanation:

Here we have , The circle
`(x+4)^2 + (y-2)^2=85` passes through the point (2,-5). We need to find that this statement is true or false . We have the following equation of circle :

`(x+4)^2 + (y-2)^2=85`

Now, In order to say that point (2,-5) passes through this circle , this point must satisfy the equation of circle i.e.
`(x+4)^2 + (y-2)^2=85` . Let's value of this point in equation of circle:

`(x+4)^2 + (y-2)^2`

⇒
`(x+4)^2 + (y-2)^2`

⇒
`(2+4)^2 + (-5-2)^2`

⇒
`(6)^2 + (-7)^2`

⇒
`36+49`

⇒
`85`

Since, on putting value of (2,-5) we get 85 , this point lies on the circle with equation
`(x+4)^2 + (y-2)^2=85` . And so statement is true!

Answer 2

A circle
`(x+4)^2+(y-2)^2=85` passes through point (2, -5) is true

Solution:

Given equation of circle is:

`(x+4)^2+(y-2)^2=85`

Given statement is:

A circle
`(x+4)^2+(y-2)^2=85` passes through point (2, -5)

We have to say whether the statement is true or false

Substitute x = 2 and y = -5 in given equation

`(2+4)^2 + (-5-2)^2 = 85\\\\6^2 +(-7)^2 = 85\\\\36 + 49 = 85\\\\85 = 85`

The point (2 , -5) satisfies the given circle equation

Thus the statement is true