Answer:
r = 10 , centre = (6, - 2 )
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 - 12x - 60 = - y² - 4y ( add y² + 4y to both sides )
x² - 12x + y² + 4y - 60 = 0 ( add 60 to both sides )
x² - 12x + y² + 4y = 60
using the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = 60 + 36 + 4
(x - 6)² + (y + 2)² = 100 ← in standard form
with centre = (6, - 2 ) and r = = 10
Answer:
I got 103˚ because I put (x+40)˚ into the calculator
Answer:
Equation of the Ellipse
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the equation
x² + 2 x + 2y² - 12 y +11 = 0
⇒ x² + 2 x + 1 - 1 + 2(y² - 6 y )+ 11 = 0
x² + 2 x + 1 - 1 + 2(y² - 2(3) y+9-9 )+ 11 = 0
⇒ x² + 2 x + 1 - 1 + 2(y² - 2(3 y ) + 3²- 3² ) + 11 = 0
By using (a +b)² = a² + 2 a b + b²
(a -b)² = a² - 2 a b + b²
<u><em>Step(ii):-</em></u>
x² + 2 x + 1 - 1 + 2(y² - 2(3 y ) + 3²- 3² ) + 11 = 0
⇒ ( x+1)² +2( y-3 )² - 1 - 2(9) +11 =0
⇒ ( x+1)² +2( y-3 )² - 8 =0
( x+1)² +2( y-3 )² = 8
Dividing '8' on both sides , we get
This equation represents the Ellipse
Answer:
Step-by-step explanation:
The conic form of the equation for a sideways parabola is
(y - k)² = 4p(x - h)
The focus is at (h + p, k)
The equation of Samara's parabola is
(y - 3)² = 8(x - 4)
h = 4
p = 8/4 = 2
k = 3
h + p = 6
So, the focus point of the satellite dish is at
The exterior angle is 180-135= 45 degrees.
The number of sides=
The number of sides= 8 sides
This is an octagon