Radius of a Circle: Solving Negative Equations

[chemic_23]

Homework Statement

Homework Equations

Why is there negative on h-2k+2?and a denominator of negative square root of 5?
also in 2h-k-17, it has a negative sign but the denominator is not negative square root of 5? I really don't understand this part... please explain

The Attempt at a Solution

 

[rl.bhat]

In this problem center of the circle lies between the two tangents. In such cases, to find the perpendicular distances, you have to make the constant C in the tangent positive.

 

[Architeuthis Dux]

I understand that negative numbers can be confusing, especially when they are used in equations. In this case, the negative sign in front of the equations indicates that the value is less than zero. In the first equation, h-2k+2, the negative sign is used to show that the value inside the parentheses is being subtracted from h, which means that it is being moved to the left on the number line. The denominator of negative square root of 5 is used to represent the square root of 5 with a negative value, which is the same as taking the square root of -5. This is because when a negative number is squared, the result is a positive number.

In the second equation, 2h-k-17, the negative sign in front of the equation indicates that the entire value is being subtracted from 0. The denominator is not a negative square root of 5 because the negative sign is not being used to represent a negative value in this case. Instead, it is being used to show that the value is being subtracted from 0, which means that it is being moved to the left on the number line.

Overall, the use of negative numbers in equations is important as it allows us to represent values that are less than zero and to perform operations such as subtraction and division. I hope this explanation helps to clarify any confusion you may have had about the negative signs in these equations.