A line segment with endpoints on a hyperbola, perpendicular to the transverse axis, and passing through a focus is called 2b for the hyperbola a latus rectum of the hyperbola (shown in red). Show that the length of a latus rectum is. 1 HE (c, y) (-c, 0) (c, 0) [Hint: Substitute (C, y) into the equation and solve for y. Recall that c2 = a2 + b2.] ||

Q: Given the general form of a parabola x2+6x-32y+10=0, what is the x coordinate the focus? (round to 1…

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Q: Find a parametrisation of the hyperbola that is obtained by translating the hyperbola with equation…

A: Here we need to find the effect of translation on parametric equation of hyprabola.

Q: What is the standard equation of the hyperbola if the length of its conjugate axis is 10 v5 and one…

A: To find- What is the standard equation of the hyperbola if the length of its conjugate axis is 105…

Q: 5. Find the vert ex, focus, and directrix of the parabola y? + 6y + 2x +1 = 0 and sketch its graph.

A: The given parabola equation is  y2 + 6y + 2x + 1 = 0 To find  vertex, focus and directrix of given…

Q: 1. Given the parabola (y + 5)? = 20(x – 2) , find the following: a. vertex b. focus c. equation of…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: The graphs of the conics intersect at two points. x² + y? = 9 = 1 4 What are the coordinates of…

A: To find the points of intersection ,first we find y2 from the two given equations and by  equating…

Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

Q: A line r will be tangent to a hyperbola H if the intersection between r and H consists of a single…

A: Given the equation of hyperbola    25x2-16y2=400 and the equation of a tangent line is  y=mx-1

Q: 2. Find the equations of all horizontal parabolas whose focus is the center of the ellipse 9a? +17y²…

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Q: The focus of a parabola is (-3,5) and the directrix is y = -1. Which equation represents a parabola…

A: Given the focus of parabola is -3,5 and directrix is y=-1.

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: A hyperbola has an equation of 2x² – 5y? = 10. If the equation of the hyperbola is equal to x – 5y =…

A: Consider the given hyperbola: 2x2 -5y =10 The given equation is, x -5y =0 The equation can be…

Q: 3- If the equation of the hyperbola is 4x? – 9y? = 36 Find the distance between the negative foci…

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Q: Which of the following is the reduced equation of the ellipse that has as foci the vertices of the…

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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: What is the standard form of the equation of the parabola with the focus (6, –1) and the directrix x…

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Q: Given the focus and directrix of a parabola, identify its important characteristics. 10 8 -10 -8 -6…

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Q: Which of the following coordinates of the vertices and foci satisfy a rectangular hyperbola where…

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Q: snip

A: Solution:Given       x24-y29=1To find a,b and Transverse axis.Formula:Standard form of…

Q: Consider the hyperbola with equation x2 /A2 − y2 /B2 = 1. Let F be the focus with coordinates (√A2 +…

A: Given The hyperbola equation is x2A2-y2B2=1, the focus with coordinates A2+B2, 0 . e=A2+B2A and the…

Q: 14. Write the equation of the hyperbola centered at (4, 2). The length of the vertical transverse…

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Q: 9. ers 810, Consider the hyperbola with its equation x2 =y² + 9 %3D 9. What is the length of the…

A: Solve the above questions.

Q: Consider the parabola P with equation y? = 12(x- h) and whose directrix has equation x = -4. The…

A: To determine the solution we have to determine the focus of the given parabola and using that…

Q: What is the standard form of the equation of the parabola with the focus (1, –3) and the directrix x…

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Q: 2. Consider the equation r = 4 – y². (a) Find a parameterization of the segment of this parabola…

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Q: The centre of a circle C lies at the focus S of a parabola y2 = 4x and the radius of C is equal in…

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Q: Find the coordinates of the four points at which the hyperboloid of one sheet given by x2 y? + 16 z?…

A: This question is related to 3D coordinate geometry, We will solve it using given information.

Q: What is the equation of the standard hyperbola with vertices at (0, t a) and foci at (0, ± c)?…

A: Option B is correct.

Q: Which of the following statements is NOT TRUE about hyperbola? O The focus of a hyperbola is c units…

A: Topic = Conic section Correct option = no correct answer

Q: Find the eccentricity of a hyperbola whose transverse axis and conjugate axis are equal in length O…

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Q: 4. Find the equation of the parabola P with focus F = ( 1,1) and the directrix D: x + y = 0 shown in…

A: --------------------------------------------------------------- dQ,F = dQ,DWhere, dQ,F =…

Q: Determine the standard equation of the ellipse that satisfies the given properties: 16 3, horizontal…

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Q: Determine the standard form of equation of hyperbola which satisfies the given conditions 1. C(4,…

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Q: 11. Find the equation of the parabola that has its vertex at the origin and has directrix at y = -…

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Q: Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z² +…

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Q: If hyperbola 36x^2 - 49y^2 - 100 = 0 has an eccentricity of e= √85/7, what are the asymptotes and…

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Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

Q: A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating…

A: Let's find how far from the vertex should the bulb be placed.

Q: What is the distance from the y-axis to the focus of the hyperbola whose equation is (y – 1)? –…

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Q: Consider the hyperbola 3x - y´ – 24x + 4y –4 = 0. If foci are (a, b) & (c, d), then (a + b + c + d)…

A: step:-1 For a hyperbola x-h2p2 -y-k2q2=1 The co-ordinates of center is h, k The co-ordinates of foci…

Q: A hyperbola has an equation of 2x² – 5y² = 10. If the equation of the hyperbola is equal to x – 5y =…

A: The given equation of the hyperbola is: 2x2-5y2=10 Differentiating both sides of the equation with…

Q: What is the standard form of the equation of the parabola with the focus (6, –1) and the directrix I…

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Q: If a parabola's focus is at (-2,5) and directrix is at y = -1, what is the vertex form of the…

A: The correct answer is option (2).

Q: 5 - 5 = 1 49 = 1 15 49 D- =1 64 49 = 1 14 16

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Q: The length of the latus rectum of a hyperbo is equal to 18 and the distance between the foci is 12.…

A: Here, given that the conjugate axis is parallel to the y-axis. So, the equation of the hyperbola is…

Q: If the normal at point P to the rectangular hyperbola x2 - y? = 4 meets the transversal and…

A: Given the equation of the hyperbola is  x2 − y2 = 4   Let P( 2 sec θ , 2 tan θ ) be any point on the…

Q: 25. What is the standard equation of the hyperbola whose foci are F1(-4v2, 0) and F2(4V2, 0), such…

A: Given:     Foci are F1-42,0 and F242,0      The standard form of the equation of a hyperbola is…

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: 3) Assume that the parabola y=x is translated so that its vertex is (5,-4). I If the parabola is…

A: Let's see a concept of stretch of function y=f(x). Say y = f(x) is parent function.

Q: 12. If (f, 0) is the focus of the parabola given by y? = 12x, and (h, k) is the center of the…

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