Solution:
Given equation of circle is:
[tex](x+4)^2+(y-2)^2=85[/tex]
Given statement is:
A circle [tex](x+4)^2+(y-2)^2=85[/tex] 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
[tex](2+4)^2 + (-5-2)^2 = 85\\\\6^2 +(-7)^2 = 85\\\\36 + 49 = 85\\\\85 = 85[/tex]
The point (2 , -5) satisfies the given circle equation
Thus the statement is true
statement is true!
Step-by-step explanation:
Here we have , The circle[tex](x+4)^2 + (y-2)^2=85[/tex] passes through the point (2,-5). We need to find that this statement is true or false . We have the following equation of circle :
[tex](x+4)^2 + (y-2)^2=85[/tex]
Now, In order to say that point (2,-5) passes through this circle , this point must satisfy the equation of circle i.e. [tex](x+4)^2 + (y-2)^2=85[/tex] . Let's value of this point in equation of circle:
[tex](x+4)^2 + (y-2)^2[/tex]
⇒ [tex](x+4)^2 + (y-2)^2[/tex]
⇒ [tex](2+4)^2 + (-5-2)^2[/tex]
⇒ [tex](6)^2 + (-7)^2[/tex]
⇒ [tex]36+49[/tex]
⇒ [tex]85[/tex]
Since, on putting value of (2,-5) we get 85 , this point lies on the circle with equation [tex](x+4)^2 + (y-2)^2=85[/tex] . And so statement is true!