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Analytic Geometry
1. A farmer wants to dig a circular reservoir for water storage. He decided to have it 10- feet wide in diameter. Is there a need for a mango tree that is located at coordinates (-4, 2) from the center of the reservoir to be removed? Support your answer.
2. Satellite dishes are usually shaped like a paraboloid, where each cross section is a parabola. This shape of the dish allows radio signals coming in parallel to the axis of the dish to bounce off the surface and meet at the focus. Hence, the receiver should be placed at the focus for a good signal reception. How far should the receiver be from the vertex if the satellite dish is 14 ft across and 5.2 ft deep at the vertex?
Analytic Geometry
The projection of a line segment AB on another line is the line segment CD, then IABl = lCDl.
True or false with full explanation
True or false with full explanation
Analytic Geometry
The xy-plane intersects the sphere x^2+y^2+z^2+2x+2y-z=2 in a great circle.
True or false with full explanation
True or false with full explanation
Analytic Geometry
The curve x^4+y^4=4a^2xy is symmetric with respect to the origin.
True or false with full explanation
True or false with full explanation
Analytic Geometry
Identify the type of the conic 4(x-2y+1)^2 +9(2x+y+2)^2 = 25
Analytic Geometry
The xy-plane intersects the sphere x^2+y^2+z^2+2x+2y-z=2 in a great circle.
True or false with full explanation
True or false with full explanation
Analytic Geometry
Find the equation of the right circular cone vwhen the straight line 2y+3z=6, x=0 revolves about the z-axis
Analytic Geometry
ABC has vertices at A(3,4), B(-2,0),and C(5,0). Prove the area of the triangle formed by joining the midpoints of ABC is one-quarter the area of ABC:
A) find the distance from the point A(5,7) to the line joining B(-2,1) and C(4,-3)
A) find the distance from the point A(5,7) to the line joining B(-2,1) and C(4,-3)
Analytic Geometry
Find the new equation of the curve (x-2)^2= y(y-1)^2 by the transforming to parallel axes through the point (2,1)
Analytic Geometry
Find the equations of the tangent planes to the conicoid 7x^2-3y^2-z^2+21=0, which pass through the line 7x-6y+9=0, z=3
