Will you please check my work for me.
1)The equation of a parabola is shown.
y=1/14X^2. What are the coordinates of the focus?
(0,3.5) <----
(0,-4)
(0,7)
(0,-3.5)
2)The equation x2 + (y + 3)2 = 36 models the boundary on a local map for which Darren can hear his friend Tom on his two-way radio when Darren is at home. How far (in miles) can Tom walk from Darren's home and still be heard?
3 miles
6 miles<----
2 miles
12 miles
3)A plane intersects only one nappe of a double-napped cone. It is neither perpendicular to the cone's axis nor parallel to its generating line. Which conic section is formed?
point
circle
ellipse <-----
parabola
No one has answered this question yet.
1) To find the coordinates of the focus of a parabola with the equation y = (1/14)x^2, you can use the standard form of a parabolic equation: (x-h)^2 = 4p(y-k), where (h,k) is the vertex of the parabola and p is the distance from the vertex to the focus.
In this case, since the equation is y = (1/14)x^2, we can see that the vertex is at the origin (0,0). To find the value of p, we can compare the equation to the standard form equation: (x-0)^2 = 4p(y-0).
By comparing the coefficients, we see that 4p = 1/14, which gives us p = (1/14)/4 = 1/56. This means that the focus is located at a distance of 1/56 units above the vertex, which gives us the coordinates of the focus as (0, 1/56).
Therefore, the correct answer is (0, 1/56), which corresponds to option (0,3.5).
2) The equation x^2 + (y + 3)^2 = 36 represents a circle with center (0, -3) and radius 6. In this context, it models the boundary on a local map for which Darren can hear his friend Tom on his two-way radio when Darren is at home.
To determine how far Tom can walk from Darren's home and still be heard, we need to find the length of the radius, which is 6 miles. Therefore, the correct answer is 6 miles, corresponding to option (6 miles).
3) When a plane intersects only one nappe of a double-napped cone, and it is neither perpendicular to the cone's axis nor parallel to its generating line, it forms an ellipse.
Therefore, the correct answer is ellipse, corresponding to option ellipse.