Answer:
centre = (- 2, 3 )
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² + 4x - 6y = 12 ( collect x/ y terms )
x² + 4x + y² - 6y = 12
using the method of completing the square
add ( half the coefficient of the x/ y terms)² to both sides
x² + 2(2)x + 4 + y² + 2(- 3)y + 9 = 12 + 4 + 9
(x + 2)² + (y - 3)² = 25 ← in standard form
with centre (- 2, 3 ) and r = 
= 5
midpoint = (2, 4 )
using the midpoint formula
midpoint = [ 
(1 + 3 ), (2 + 6 )] = (2, 4)
Let me think this again and I will get back later!! 2.234 graph
Answer:
B. 6√2
Step-by-step explanation:
We can use the Pythagorean Theorem to solve this out. The Pythagorean Theorem states that for any right triangle with the shortest sides (called legs) as a and b and the longest side (called the hypotenuse) as c:
a² + b² = c²
Here, a = b = 6, so:
6² + 6² = c²
36 + 36 = c²
72 = c²
c = √72 = 6√2
Now, we see the answer is B.
However, there's a trick to solving these kinds of problems. Notice that DEF is both an isosceles triangle and a right triangle. We call these 45-45-90 triangles because those are the angles of the triangle.
One characteristic of these types of triangles is that their leg to leg to hypotenuse ratio is 1 : 1 : √2, always. We could apply that here. We see that the legs are 6, so we could find the hypotenuse simply by multiplying 6 by √2, and we would get 6√2, which is exactly the value we obtained above.
Thus, the answer is B.
