Answer:
the equation of the hyperbola is;(x²/81) - (y²/1600) = 1
Step-by-step explanation:
We are given that the hyperbola has;
Centre; 0,0
Vertex; 9,0
Focus; 41,0
Thus,the vertex and focus are on the x-axis. Thus, the equation for the hyperbola will have the form;
(x²/a²) - (y²/b²) = 1
Since The vertex is (9,0),so
a = 9 and a² = 9² = 81
Also,Since The focus is (41,0),so
c = 41 and c² = 41² = 1681
Solving for b², we have;
b² = c² - a²
b² = 1681 - 81
b² = 1600
b = √1600
b = 40
Thus,equation of hyperbola is;
(x²/9²) - (y²/40²) = 1
Which gives;
(x²/81) - (y²/1600) = 1
If I am rolling a single dice what is the probability of rolling a number that is divisible by 2 and 3? The only number divisible by 2 and 3 is 6. So, would the answer be 1 out 6 or 1/6
![\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ -\cfrac{1}{4}(y+2)^2=x-7\implies -\cfrac{1}{4}[y-(-2)]^2=x-7 \\[2em] [y-(-2)]^2=-4(x-7)\implies [y-(\stackrel{k}{-2})]^2=4(\stackrel{p}{-1})(x-\stackrel{h}{7})](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5C%5C%5C%5C%204p%28y-%20k%29%3D%28x-%20h%29%5E2%20%5Cend%7Barray%7D%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20vertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20-%5Ccfrac%7B1%7D%7B4%7D%28y%2B2%29%5E2%3Dx-7%5Cimplies%20-%5Ccfrac%7B1%7D%7B4%7D%5By-%28-2%29%5D%5E2%3Dx-7%20%5C%5C%5B2em%5D%20%5By-%28-2%29%5D%5E2%3D-4%28x-7%29%5Cimplies%20%5By-%28%5Cstackrel%7Bk%7D%7B-2%7D%29%5D%5E2%3D4%28%5Cstackrel%7Bp%7D%7B-1%7D%29%28x-%5Cstackrel%7Bh%7D%7B7%7D%29)
so h = 7, k = -2, meaning the vertex is at (7, -2).
the squared variable is the "y", meaning is a horizontal parabola.
the "p" distance is negative, for a horizontal parabola that means, it's opening towards the left-hand-side.
we know the focus and directrix are "p" units away from the vertex, and we know the parabola is opening horizontally towards the left-hand-side.
the focus is towards it opens 1 unit away, at (6, -2).
the directrix is on the opposite direction, 1 unit away, at (8, -2), namely x = 8.
1) 2a = 9b ⇒ 2:9
2) a + b = 3b ⇒ a = 2b ⇒ 1:2
Answers: 2:9 and 1:2
Answer:
The answer is B.) x=1, y=2
Step-by-step explanation:
2(1)+2=4
3(1)+3(2)=9
