The filament lightbulb is a thin wire that glows when electricity passes through it. The filament of a car headlight is at the focus of a parabolic reflector, which sends out in a straight beam. Suppose that the reflector is 7 inches wide and 2 inches deep. If the filament is placed 1.25 inches from the vertex, will it be able to send out light in a straight beam? At what point, relative to the bulb's vertex should the filament be placed?

Q: Find the coordinates of the foci for the following hyperbola. (x – 5)2 (y + 7)² = 1 16 25

A:

Q: Find the equation of the Hyperbola whose Foci are at (6,4) and ( 30,4),and the length of its…

A:

Q: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

Q: Find the equation of the parabola with a focus at (1, -8) and a vertex at (1, - 2). Let a represent…

A: Since the x-coordinates of the vertex and focus are the same, they are one of top of the other. So,…

Q: Graph the given parabola and find its focus: Y=X squared

A: The given equation of parabola is: y=xory2=x  where x > 0

Q: In which direction do the following parabolas open?a. y2 = -4x        b. x2 = 4y

A: Part(a) Given parabola  The graph of the given parabola is

Q: Find the standard equation of the parabola which satisfies the given condition. Focus (7, 11),…

A:

Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Given a focus of (2, 4) and a directrix of y= -2, find the equation for the parabola. (2-

A: Given:    focus (2 , 4)    directrix y = -2

Q: Please

A: Now differentiate it with respect to y and equate it to 0.

Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

Q: If the directrix of a parabola is x = 2, and the focus is (−4, 0), determine the focal length and…

A: Draw the focus (-4,0) and directrix x=2 Distance from focus to directrix is 2-(-4)= 6 Focal length…

Q: Given a parabola's focus at (6, −4) and directrix at y = −7, how would you write its equation?

A: Equation of parabola: x-h2=4py-k Where vertex is (h, k) Focus is (h, k+p) And directrix y = k - p

Q: For the ellipse b'x' + a'y a'b?, show that the equations of its tangents of slope m

A:

Q: B. C.

A: Given point A= (1,-2)

Q: A doomed ceiling is a parabolic surface. Ten meters down from the top of the dome, the ceiling is 15…

A: Given a doomed ceiling is a parabolic surface which is 10m down from top and 15m wide. A light is…

Q: What is the standard equation of the hyperbola if the length of its transverse axis is 12 and one of…

A:

Q: State the equation of the parabola which has a focus of (9, 3) and a directrix of y = -3. (Let a be…

A: To find the equation of the parabola having focus and a directrix, let we choose (x, y) be any point…

Q: Given hyperbola   (y + 1)2   −   (x − 2)2   = 1       9                4         what will its…

A: Given: An equation of the hyperbola, y+129-x-224=1.

Q: Which of the following correctly depicts the sphere given by the equation: x2 + (y - 2)2 + (z - 2)2…

A: Given: x2 + (y - 2)2 + (z - 2)2 = 4

Q: The Cassegrain telescope design (dating back to 1672) makes use of the reflective properties of both…

A:

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

A: Given directrix: x=0 and focus (-4,5)The vertex will be the mid point of them Mid point of x=0 and…

Q: Suppose that two people standing 2 mi (10,560 ft) apart at points A and B hear a car backfire. The…

A:

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

A:

Q: Find the shortest distance from the point (1,4) to a point on the parabola y =2 x (a) /2 (b) 1 (c) 2…

A: To determine the shortest distance between point and the parabola,

Q: The Hubble Space Telescope was launched into space in 1990 and now orbits the Earth at 5 mi/sec at a…

A:

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

A:

Q: satellite dish shaped like a paraboloid, has a diameter 2.4ft and depth 0.9ft. If the receiver is…

A:

Q: find the points on the parabola y=x^2 closest to the point (0,1)

A:

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

A: To find the equation of the standard form of parabola Focus -10,0 Directrix x=10

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(2, 0), directrix x = -2

A: If the coordiantes of the focus h+p,k and directrix x=h-p Then, equation of parabola y-k2=4px-h We…

Q: Indicate whether the following equations define a straight line (L), a circle (C), an ellipse (but…

A: Concept of identifying the equation Circle for the equation of circle, both x and y are squared…

Q: Find an equation of the parabola that satisfies the conditions. a) Focus (0, -) and directrix, y =…

A: Given  Focus (0 , -1/2)  Directrix ,y = 1/2   Equation of parabola with focus at (x0 , y0) and…

Q: 2. A parabolic antenna has a width across the top of 36 inches and the depth at the center is 6…

A:

Q: Suppose that two microphones 1500 m apart at points A and B detect the sound of a rifle shot. The…

A: We have the figure as:

Q: Find the following points of intersection. The point(s) of intersection of the parabola y = x2 + 2…

A: Given equation of parabola is y=x2+2 and equation of line is y=x+4. We have to find point of…

Q: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

A:

Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

A:

Q: Explain why the dots in Figure 23 lie on a parabola. Where are the focus and directrix located? y=…

A:

Q: Find the equation of Hyperbola using only the following information: Center at (0, 0) Vertices at…

A:

Q: The parabola y=x^2y=x2y, equals, x, squared is shifted up by 777 units and to the left by 111 unit.…

A:

Q: Find the equation of Parabola and Graph with the following information: Center at (0, 0) Vertices…

A:

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (7,…

A: Parabola: The focus of the parabola is (7,1) Directrix of the parabola is y=-9. The equation of…

Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: The path of the basketball through from the hoop is modeled by the parabola,

Q: What will be the equation of hyperbola that satisfies the given condition foci at (+ 24,0) and the…

A:

Q: The signal received by a parabolic antenna is concentrated in its receiver, which is placed,…

A: For the Paraboloid,z-axis is it's Principal Axis,Also, it is symmetric with the lines x = 0 (yz…

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (2,…

A: Consider trhe focus of the parabola is 2,4 and the directrix is x=-4. Let x,y be any point on the…

Q: A parabolically shaped bookshelf has a width of 14 feet 8 inches at the top and height 8 ft. 4 in..…

A: Consider the given information as, width=14feet  8 inches and height =8ft 4 in

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.