A cross-section of a design for a travel-sized solar fire starter is shown in the picture. The sun’s rays reflect off the parabolic mirror toward an object attached to the igniter. Because the igniter is located at the focus of the parabola, the reflected rays cause the object to burn in just seconds. Assume that the vertex of the parabolic mirror is at the origin of the coordinate plane. Find the equation of the parabola that models the fire starter.

Q: Classify the graph of the equation 9x2 + 9y2 − 36x + 6y + 34 = 0 as a circle, a parabola, an…

A: Since the coefficients of x2 and y2 are the same and are of the same sign too. So this given…

Q: Find the standard form equation of the parabola with the given characteristics and a vertex at the…

A: Topic = parabola

Q: Find the focus and directrix of the parabola with the given equation y2 - 6x=0. Then graph the…

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Vertex: (5,…

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Q: Find the standard form of the equation of a parabola with focus (5,0) and directrix x = -5,shown in…

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Q: Find the standard form of the equation of the parabola with the given characteristics.

A: From the given diagram, it is clear that vertex, (h,k) = (2,6) and the distance from x-axis is p=2…

Q: Solve for the equation of the parabola described. Vertex at (2,4); focus at (2,-1)

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Find the focus and directrix of the parabola with the given equation 8y2 + 4x = 0. Then graph the…

A: We have the given equation of a parabola   The equation is 8y2 + 4x = 0   We know that the…

Q: Find the equation of the hyperbola having center at the origin with transverse axis on the x-axis,…

A: Given-  Hyperbola having center at the origin with transverse axis on the x-axis, a=4, and latus…

Q: suppose that the bulb of a flashlight is placed at the focus of its parabolic reflector. if the…

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Q: Find the focus and directrix of the parabola with the given equation y2 = -12x. Then graph the…

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Q: The cables that hold up a suspension bridge form a parabola. The distance between the towers is 600…

A: Given that, the distance between towers as 600 feet and the height of each tower is 500 feet from…

Q: Find the vertex, focus, directrix, and focal width of the parabola. x2 = 28y

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Q: Write the equation of a parabola whose directrix is æ 0.25 and has a focus at (1.75, 6)

A: Given, The parabola whose  Directrix is x = 0.25 Focus at 1.75, 6  We have the write the equation…

Q: Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and…

A: The standard equation of hyperbola with center (0,0) and having horizontal transverse axis is given…

Q: Find an equation for the ellipse that shares a vertex and a focus with the parabola y2 + 4x = 36 and…

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Q: Find the equation of the parabola with a vertex at (2,1)  and focus at (2,3). Explain how to graph…

A: Topic:- parabola

Q: Find the standard form of the equation of the parabola with the given characteristics. Focus: (2,…

A: Given that the directrix is x = -2, we can conclude that the parabola opens to the right(in a…

Q: A cable TV receiving dish is in the shape of a paraboloid of revolution (3D parabola). Find the…

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Q: Find the standard form of the equation of the parabola. Vertex at the origin, focus at (0, 8)

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Q: Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and…

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Q: The line segment perpendicular to the axis of symmetry, passing through the focus and with endpoints…

A: Given:The line segment perpendicular to the axis of symmetry, passing through the focus and with…

Q: find the focus, directrix, and focal diameter of the parabola, and sketch its graph  a. x= -8y² b.…

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Q: Determine the equation of the parabola using the given information. Focus (0, −3) and directix y =…

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Q: Find the vertex, focus, and directrix for the parabola.

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Q: Write the standard equation of parabola with the focus at (-1, 2) and the vertex (1,2) Determine :…

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Q: Find the equation of the parabola in standard form with focus at (7, -6) and vertex 5 units at the…

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Q: Determine the standard form of an equation of the parabola with focus (1, 2) and directrix x = 7.

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Q: Find a Cartesian equation for the curve and identify it as either a hyperbola, circle, limaAson,…

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Q: Find the standard form of the equation of a parabola with focus (8,0) and directrix x = -8.

A: Focus is, a, 0=8, 0⇒a=8 Directrix is x=-8.

Q: Which equation represents the parabola graphed on the coordinate plane below?

A: NOTE: Refresh your page if you can't see any equations. . compare this equation with the vertex form…

Q: Write the equation of the parabola with the focus at (−4, 0) and the directrix is x = 4

A: Given that Focus (-4,0) and the directrix is x=4 and we find equations of parabola.   Here i…

Q: Find the focus and directrix of the parabola with the given equation y2 - 6x = 0. Then graph the…

A: Given equation of the parabola is: y2 - 6x = 0 y2 = 6x  y2 = 4 . (3/2) . x  Therefore the focus of…

Q: Find the vertex, focus, and directrix of the parabola (x-3)2=12(y+1) and sketch the graph of the…

A: The graph of given parabola is graphed in the step 2.

Q: Find the standard form of the equation of the parabola with the given characteristics and vertex at…

A: given,      parabola with the given characteristics and vertex at the origin. Focus: (0, 1/3)

Q: find the standard form of parabola from the given points.  vertex(3,1)     focus(0,1)

A: To find the standard form of parabola having vertex (3,1) and focus (0,1). Solution: The standard…

Q: If the directrix is horizontal, then the parabola opens (horizontally/vertically).

A: Given:We must find the missing word in the given sentence.So, Definition of parabola said:A parabola…

Q: Find the focus and directrix of the parabola y = -x2, and sketch the graph.

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Q: Derive an equation for the parabola with focus (a , b) and directrix x = c

A: Given focus f =(a,b) and directrix x=c Let A(x1,y1) be any point so that  |Af|= |AD| Where Af=…

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (+11, 0), vertices:…

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Q: Find the standard form of the equation of the parabola. Vertex at the origin, focus at (2, 0)

A: General equation of horizontal parabola is given by -y-k2 = 4px-h             ..........(1)where, h,…

Q: Find the vertex, focus, foci and directrix of the parabola (x-6)^2+8(y+7)=0 and sketch its graph

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Q: Write the equation of a parabola in standard form from the given information Focus at (-5,7)…

A: Since , focus lies on x-axis Therefore , equation is either y2=4ax or y2=-4ax Now focus has negative…

Q: Find the standard equation of the parabola which satisfies the given conditions. Focus (-2, -5),…

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Q: Find the equation of a parabola that has focus at (-4,0) and directrix 2

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Q: Find the focus, directrix, and focal diameter of the parabola y = x², and sketch its graph.

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Q: if the radio signal travel at a speed of 980ft/ms , find an equation of the hyperbola on which the…

A: Consider points A & B are two sending station and K is the of the ship, and suppose two-point be…

Q: Find the focus diretrix, and focal diameter of the parabola: x^2=-8y

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Q: Find the vertex, focus, and directrix of the parabola (x − 6)2 − 2( y + 7) = 0, and sketch its…

A: Given: The equation of the parabola is, x-62-2y+7=0 The above equation can be converted into vertex…

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.