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
The answers are correct. At least that's what my father thinks. He said he is 100% sure.
Sure, I'd be happy to help you check your work.
1) To find the coordinates of the focus of a parabola, you need to know its equation in the form "y = ax^2 + bx + c". However, the equation you provided is "y = (1/14)x^2". The focus of a parabola is given by the formula (h, k) where h = -b/2a and k = c - (b^2 - 1)/4a.
Since the equation you provided does not have a linear term (bx), we can assume that b = 0. Therefore, the focus of the parabola is at (h, k) where h = 0 and k = 1/4a. Plugging in a = 1/14, we get k = 14/4 = 3.5.
So, the correct answer is (0, 3.5).
2) In order to determine how far Tom can walk from Darren's home and still be heard, we need to consider the equation x^2 + (y + 3)^2 = 36. This equation represents a circle with its center at (-0, -3) and a radius of 6 units.
The radius of the circle represents the maximum distance that Tom can walk from Darren's home and still be heard. Therefore, the correct answer is 6 miles.
3) A plane that intersects only one nappe of a double-napped cone, which is neither perpendicular to the cone's axis nor parallel to its generating line, will form an ellipse.
Therefore, the correct answer is ellipse.
I hope this helps! Let me know if you have any more questions.