Answer:
<h2>The standard form: x² + (y + 1)² = 25</h2><h2>The general form: x² + y² + 2y - 24 = 0</h2>
Step-by-step explanation:
The equation of a circle:
(h, k) - center
r - radius
We have the center (0, -1) and the radius r = 5 <em>(look at the picture)</em>.
Substitute:
<em>use (a + b)² = a² + 2ab + b²</em>
<em>subtract 25 from both sides</em>
You can write the equation using conventional symbols as
3x^2 - 2x - 5 = 0
You can recognize that the middle coefficient is equal to the sum of the other two, so those two coefficients can be used to factor the equation.
(1/3)(3x +3)(3x -5) = 0 . . . . . put the coefficients in the form (1/a)(ax + ...)(ax + ...) (x+1)(3x-5) = 0 . . . . . simplify
The solutions are the values of x that make one or the other of the factors equal to zero.
x = -1
x = 5/3
4+I-15I÷3
4+15÷3
4+5
9
The answer is 9
let us represent the question with a diagram for better understanding.
Using Pythagoras theorem
![\begin{gathered} c^2=12^2+9^2 \\ c^2=144+81 \\ c=\sqrt[\square]{225} \\ c=15\text{ km} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%5E2%3D12%5E2%2B9%5E2%20%5C%5C%20c%5E2%3D144%2B81%20%5C%5C%20c%3D%5Csqrt%5B%5Csquare%5D%7B225%7D%20%5C%5C%20c%3D15%5Ctext%7B%20km%7D%20%5Cend%7Bgathered%7D)
The distance between the parents and grandparent house = 15 km
