If the normal at point P to the rectangular hyperbola x2 - y? = 4 meets the transversal and conjugate axes at A and B respectively and C is the center of the hyperbola, then O PA = PC O PA = PB O AB = 2PC O PB = PC

Q: A hyperbola has its vertices at (0, 4) and (0, - 4), and one focus is at (0, What equation describes…

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Q: If e and e' be the eccentricities of the hyperbola and its conjugate. 1 1 prove that = 1. e? e?

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Q: satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: We will solve the following.

Q: Which of them are tr 1) Ellipsoid de + 16: Hyperbakid II) =D4- Sy-9 Perbled IV) Sphere

A: The equation of ellipsoid is of the form x2a2+y2b2+z2c2=1 So, (I) is true.

Q: IS filled with circley The world around us Para bolas , e llipses and hyperbolas, In your post…

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Q: Find the standard form of the equation of the specified ellipse. 19. Foci: (0, –4). (-4, – 4); Major…

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A: Given statement: A                  is the set of points P in the plane such that the ratio of the…

Q: Give ONE example of a plane P that is parallel to one of the coordinate planes (the ry-, xz- or…

A: The given equation of the Hyperboloid can be modified as shown below: x28-y24-z23=1    ⇒…

Q: A hyperbola has its vertices at (0, -1) and (4, -1) and its foci at (-2, -1) and (6, -1). What are…

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Q: Explain why it is not possible for a hyperbola to have foci at (0, -2) and (0, 2) and vertices at…

A: The standard form of the equation of a hyperbola with center (0,0) and transverse axis on the y-axis…

Q: If AB is a double ordinate of the hyperbola *- y =1 such b? a* that AOAB (O is the origin) is an…

A: Introduction :

Q: Identify the type of conic, assuming a > 0: r = 1+ V7sine Ellipse. O Parabola. O Hyperbola.

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Q: Find the eccentrici ty, foci, and directrices of the hyperbola y2 - x? = 4.

A: We have to find the eccentricity, foci and directrices of the given hyperbola y2-x2=4.

Q: The eccentricity e of a hyperbola is defined as the number c/a,         where ais the distance of a…

A: Given :             The eccentricity of a hyperbola is defined as a number of ca

Q: Using the property of Re z and Im z to show that the hyperbola x2 - y2 = 1 can be written as: z² + (…

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Q: = 1 10 12 = 1 20 12 x2 = 1 100 36 =1 100 144

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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: Determine the focal distance of a hyperbola if the length of the transverse and conjugate axes are…

A: The focal distance of a hyperbola is 17units.

Q: Find the length of a,b,c of the given hyperbola: x^2/4 - y^2/5=1

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Q: Determine the standard form of equation of a hyperbola with foci at (-1,0), (1,0) and one of its…

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Q: Find an equation for the hyperbola that has its center at the origin and satisfies the given…

A: Given: Foci F0,±5, conjugate axis of length 4 For given data transverse axis is on y-axis and…

Q: 2. Determine the orthogonal trajectory of the family of hyperbolas y? – 121x? = c. Sketch some of…

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Q: If PQ is a double ordinate of the hyperbola a2 1 such that AOPQ 62 is equilateral, O being the…

A: Let the hyperbola be x2a2-y2b2=1 and any double ordinate PQ be asecθ, btanθ , asecθ, -btanθ  and O…

Q: Find the spherical equation for the hyperboloid of two sheets x² – y² – 2² = 1.

A: Given information :  Equation of hyperboloid of two sheets x2-y2-z2 = 1

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: The hyperbola with vertices at (0, 3) and (o, - 3) and foci at (0, 5) and (0, - 5) has the equation…

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Q: The distance from the center to a vertex of the hyperbola 4 16 is

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Q: . If the center of the hyperbola is (2, 1) and c = 5, then the coordinates of the foci…

A: The general equation of conic section is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. The standard form of the…

Q: 17 Select the conic section represented by the equation. 4x 2 -y 2 + 24x + 4y + 28 = 0. circle…

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

A: Given-  Hyperbola with vertices at (0, ±a) and foci at (0, ±c). To find- The standard equation of…

Q: Show that the ellipse 4x + 9y = 45 and the hyperbola x - 4y = 5 are orthogonal %3D

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Q: İThe hyperbola with vertices at (0, 3) and (0, - 3) and foci at (0, 5) and (0, - 5) has the equation…

A: The objective of the question is determine the equation of the hyperbola and choose the correct…

Q: 4. Classify the following conics as a circle, parabola, ellipse or hyperbola and explain why. a) 9x?…

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Q: 7. that has its center at the origin and satisfies the given condition. Vertices V(0,±3) and foci…

A: A detailed solution is given below.

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

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Q: The center of the hyperbola is at the origin and its transverse axis is on the y-axis. One focus is…

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Q: Determine the length of the latus rectum and distance between the foci of the conic section: 16x^2…

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Q: What is the equation in standard form of a hyperbola with center C(- 1, – 3), a focus at and a…

A: In this case transverse axis is y axis.

Q: Consider the hyperboloid of two sheets of equation x23−y23−z22=1. Mark the alternative that…

A: Hyperboloid of two sheets has equation :-    ax2 - by2 - cz2 = 1    comparing with above equation…

Q: Using the property of Re z and Im z to show that the hyperbola x2- y2 = 1 can be written as: z? +…

A: We know that x=Re(z)=z+z2 and y=Im(z)=z-z2i. We are given the equation of hyperbola x2-y2=1.

Q: The hyperbola with vertices at (0, 3) and (0, – 3) and foci at (0, 5) and (0, – 5) has the equation…

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Q: Consider the conic (a hyperbola) of equation 7x – 6xy – 7y² + 13x + 25y – 60 = 0 whose graph is…

A: We have to find the equation of the tangent lines to the hyperbola at the given point.

Q: From a point P on a rectangular hyper hyperbola at A and B. Show that the a constant, independent of…

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Q: Find an equation in standard form for the hyperbola with foci at(+8, 0), transverse axis with length…

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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: 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: Eliminate the parameter 0 and obtain the standard form of the rectangular equation. hyperbola: x = h…

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Q: A hyperbola in standard position has equation 9x 2 − 15y 2 − 16 = 0. Write down a parametrisation…

A: We will first parametize the curve

Q: The vertices of hyperbola: 9z? – 4y² = 36, will be Select one: O (0, ±3) O (12,0) O (+3,0) O (0, ±2)

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