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Determine whether the statement is true or false.

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

Determine whether the statement is true or false. The circle (x+4)^2=85 passes through-example-1
User Jyvet
by
7.0k points

2 Answers

0 votes

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!

User Viveksuggu
by
7.1k points
6 votes

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

User Irvin Zhan
by
7.2k points
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