Answer:
Step-by-step explanation:
15 plus 15 plus 15 is 45 - 15 =30
The least common multiple is 63.
Explanation: 63 is the least number that 3 7 and 9 can go into evenly. Therefore, it is the least common multiple.
16x^2 + 25y^2 + 160x - 200y + 400 = 0 Rearrange and regroup.
(16x^2 + 160x) + (25y^2 - 200y ) = 0-400. Group the xs together and the ys together.
16(X^2 + 10x) + 25(y^2-8y) = -400. Factorising.
We are going to use completing the square method.
Coefficient of x in the first expression = 10.
Half of it = 1/2 * 10 = 5. (Note this value)
Square it = 5^2 = 25. (Note this value)
Coefficient of y in the second expression = -8.
Half of it = 1/2 * -8 = -4. (Note this value)
Square it = (-4)^2 = 16. (Note this value)
We are going to carry out a manipulation of completing the square with the values
25 and 16. By adding and substracting it.
16(X^2 + 10x) + 25(y^2-8y) = -400
16(X^2 + 10x + 25 -25) + 25(y^2-8y + 16 -16) = -400
Note that +25 - 25 = 0. +16 -16 = 0. So the equation is not altered.
16(X^2 + 10x + 25) -16(25) + 25(y^2-8y + 16) -25(16) = -400
16(X^2 + 10x + 25) + 25(y^2-8y + 16) = -400 +16(25) + 25(16) Transferring the terms -16(25) and -25(16)
to other side of equation. And 16*25 = 400
16(X^2 + 10x + 25) + 25(y^2-8y + 16) = 25(16)
16(X^2 + 10x + 25) + 25(y^2-8y + 16) = 400
We now complete the square by using the value when coefficient was halved.
16(x-5)^2 + 25(y-4)^2 = 400
Divide both sides of the equation by 400
(16(x-5)^2)/400 + (25(y-4)^2)/400 = 400/400 Note also that, 16*25 = 400.
((x-5)^2)/25 + ((y-4)^2)/16 = 1
((x-5)^2)/(5^2) + ((y-4)^2)/(4^2) = 1
Comparing to the general format of an ellipse.
((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1
Coordinates of the center = (h,k).
Comparing with above (x-5) = (x - h) , h = 5.
Comparing with above (y-k) = (y - k) , k = 4.
Therefore center = (h,k) = (5,4).
Sorry the answer came a little late. Cheers.
Answer:
y-intercept = (0, - 3)
x-intercept = (-6, 0)
slope = - 1/2
Step-by-step explanation:
The y intercept is the value of y when the x = 0. By looking at the graph, we can tell that when x = 0, y = - 3. Likewise for the x-intercept.
We can use the slope formula to determine the slope.
m = y2 - y1/ x2 - x1
You can choose any 2 points on the line and substitute in the formula. I chose the y and x intercepts for easier calculations.
m = - 3 - 0/ 0 - (- 6)
m = - 3/ 6
m = - 1/2
The Power of a Point theorem tells us, if we draw a line from a certain point, no matter which line we choose, the product of the two distances from the point to the line's intersections with the circles will be constant (or, if the line is tangent to the circle, the value will be equal to the square of the distance to the point of tangency). So,applying the tangent rule to the
-distance intersection and the two-intersection rule to the other, we have
, so taking the square root of the equation gives
.
