Find the product of the distances from each point on the hyperbola - = 1 to the asymptotes. a?b? A) a2-b2 a²b² В) a2+b2 ab C) a2+b? ab D) a²-b2 E) a²b²

Q: What are the vertices and foci of the hyperbola (x - 9)2/25 - (y + 6)2/144 = 1 Show all work.

A: We have to find the vertices and foci of the given hyperbola.

Q: Give the property that defines all parabolas.

A: A parabola is a plane curve and it is mirror-symmetrical and approximately it can be in the shape of…

Q: .what does the axis of symmetry do to the parabola?

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Q: Find an equation of the hyperbola satisfying the indicated properties.

A: Given :              Focus = 26, 0              Asymptote lines:…

Q: The chord of a parabolic arch is 10 cm and is 12 cm from the vertex. Calculate the perimeter of the…

A: The formula for perimeter of parabola is P=12b2+16a2+b28aln4a+b2+16a2b, where a is the distance of…

Q: What is the distance between the vertices of the hyperbola with one focus at (-1, 4) and co-vertices…

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Q: The four foci of the hyperbola 1 and its conjugate are joined to 62 form a parallelogram. Find the…

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Q: If the center of a hyperbola with a horizontal transverse axis is (2, 3) and a² = 25, then the…

A: Given Center of horizontal tranverse axis of hyperbola=(2,3)That is (h,k)=(2,3)And a2=25To find co-…

Q: For a hyperbola, the foci lie on a line called the_________

A: Given that, A statement, " For a hyperbola, the foci lie on a line called the ______ ."

Q: What is the standard form equation of the hyperbola that has vertices (0,±2) and foci (0,±/29)?

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Q: Graph a hyperbola that opens in the x direction and is centered at at (-2, 1).

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Q: Determine the coordinates of the foci of the hyperbola 9x² - 4y² - 90x + 189 = 0

A: The given equation of hyperbola          9 x^2 - 4 y^2 - 90 x + 189 = 0 ...............( 1)  First…

Q: What is a hyperbola?

A: Consider the given "hyperbola"

Q: What must be true of the foci of a hyperbola? The foci must lie --Select--- of the hyperbola and…

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Q: The cables of the middle part of a suspension bridge are in the form of a parabola, and the towers…

A: Explained below

Q: the chord joining points the A(x) and B(B) on the hyperbola -= 1 is a focal chord, then prove at…

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Q: .כ Find the ared of a parabola which is inscribed in a rectangle 40 cm long and 25 cm wide.

A: We know are of parabola is( 2/3) ×b×h Where b is base of parabola and h is height of parabola.

Q: Any point on the parabola can be labeled (x, y), as shown. 4 3 2 (*, y) ¢ -6 -5 -4 -3 2 - 1 2 3 4 5…

A: According to figure equation of parabola in standered form X2=4bYnew equation of…

Q: A triangle is inscribed in a rectangular hyperbola such that the tangent at one of the vertices is…

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Q: A rectangle is inscribed in the parabola y=8– x - such that one side lies on the x-axis and two…

A: Answer

Q: What is the directrix of a hyperbola?

A: We need to explain what is meant by directrix in hyperbola and find its equation.

Q: Show that an ellipse has exactly 4 vertices, unless it is a circle.

A: Consider an equation of ellipse x2a2+y2b2=1 where a,b>0. In parametric form, its equation can be…

Q: The line segment between the vertices of a hyperbola is called the _____ axis.

A: The difference in the distance between a point (x, y) and the two fixed points is a positive…

Q: Give the geometric definition of a hyperbola.

A: Given: Give the geometric definition of a hyperbola.

Q: A satellite dish has a shape called paraboloid, where each cross section is parabola. Since the…

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Q: What is the distance between the foci of the hyperbola with foci at (2-√13,3)and (2+√13, 3) and…

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Q: A hyperbola is the set of points in a plane, the difference of whose distances from two fixed points…

A: Given : A hyperbola is the set of points in a plane the difference of whose distances from two fixed…

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: a building facade is in the shape of a semi ellipse, with the major axis as the span. if the span is…

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Q: From any point (N) on a hyperbola, the combined distances to the foci (f1 and f2) is equal to what?

A: A hyperbola is two curves that are like infinite bows. Looking at just one of the curves: any point…

Q: The lengths of the major and minor axes of an ellipse are 10 m and 8 m, respectively. What is the…

A: Topic  =Geometry

Q: How many arrangements can be made using 4 letters of the word HYPERBOLAS if no letter is to be used…

A: There are total 10 letters in the word HYPERBOLAS. Here arrangement is being considered. So we will…

Q: How many arrangements can be made using 2 letters of the word HYPERBOLAS if no letter is to be used…

A: To find the number of arrangements which can be made using two letters of the word HYPERBOLAS if…

Q: Find the length of so-called semicubical parabola y = x3/2 on [5.2,9.6].

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Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: If the focal length of a parabola is 6 units and the vertex is (3, 2), is it possible to determine…

A: Focal length of a parabola is 6 units and the vertex is (3, 2).

Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5), and…

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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: The line segment perpendicular to the transverse axis passing through the center of a hyperbola, and…

A: Consider a parabola figure

Q: Determine the Vertices and Foci of the Hyperbola 9x - 4y = 36 %3D and Sketch.

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Q: What is the length of the transverse axis of the hyperbola whose foci are (0,-5) and (0,5), and…

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Q: The points where a hyperbola intersects the line through the foci are called the _____

A: The line through the foci is the major axis. Where it cuts the hyperbola is the vertices.Answer: The…

Q: If the center of a hyperbola with a horizontal transverse axis is (2, 3) and a2 = 25, then the…

A: Center of the hyperbola is, h, k=2, 3⇒h=2  &  k=3&a2=25⇒a=5 Therefore vertices are, h-a, k…

Q: Write the equation of the hyperbola of foci F1(2, −1), F2(2, 4) and focal radius difference equal to…

A: The equation of hyperbola can be obtained from the foci and the vertices or other parameters. If the…

Q: 40. y² – 16x² + 64x 208 = 0

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Q: What is the perimeter of the central rectangle for the hyperbola -16x² + 9y² + 96x + 54y – 207 = 0?…

A: Given:      -16x2+9y2+96x+54y-207=0        y-k2a2-x-h2b2=1 is the standard equation for up-down…

Q: . Find the vertices of the hyperbola. 16x2 - 9y? = 144 %3D (0, O (0, - 3) and (0, 3) O (0, - 4) and…

A: This question is related to hyperbola, We will solve it using given information.

Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 260 meters.…

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