Determine the eccentricity of a hyperbola with a vertical transverse axis of length 48 units and asymptotes y = 1x

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of parabola is F0, 1. Directrix is y=-1. We have to prove that y=14x2 is the…

Q: Do I have to use the equations for the asymptotes of a hyperbola centered at the origin, y = tr or y…

A: The equations for the asymptotes of a hyperbola centered at the origin is y = ±bax or y = ± abx.…

Q: find the equation of hyperbola with center (4,-1), transverse axis parallel to the y axis distance…

A: Given: A hyperbola with center 4, -1 , whose transverse axis is parallel to the y-axis. The…

Q: Find the equation of the hyperbola in standard form centered at the origin with a vertical…

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

A: A hyperbola has two curves that do not touch each other.  A hyperbola is a curve whose equation is…

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Foci: (±5,…

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Q: 8. Determine the Equation of the Hyperbola if the Transverse Axis is 8 and the Foci are at (0, ±6)

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Q: Find an equation of the hyperbola that has foci at (0,-13) and (0,13), and asymptotes y=5/12x and…

A: The hyperbola that has foci at (0,-13) and (0,13), and asymptotes y=5/12x and y=-5/12x. To find…

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 2) and directrix…

A: Given:            Focus of parabola is : F(0,2)Directrix is:​y=−2.

Q: Find an equation of the hyperbola that has foci at (-15, 0) and (15, 0), and asymptotes y= x and y=

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Q: Find an equation of the hyperbola having foci at (4-√52,5) and (4+√52,5) and asymptotes at y=3/2x+11

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Q: Explain how to use directrix. ey = &x to find the parabola's focus and

A: Given equation of parabola is y2=8x. To find focus and directrix of parabola. Solution: Equation of…

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: Show that the horizontal traces of the ellipsoid are ellipses of the same eccentricity (apart from…

A: To show Horizontal traces of the ellipsoid x2a2+y2b2+z2c2=1are ellipses of  same eccentricity

Q: 10. All hyperbolas center at the origin.

A: we know the equation of hyperbolas center at origin is…

Q: draw the ellipse when the distance of its focus from its directrix is equal to 60mm and eccentricity…

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Q: Find the equation of the parabola with focus at (5, 0) and directrix x = −5.

A: Focus lies on x-axis.

Q: 9. Find the standard form of the equation of the parabola with a focus at (-3, 4) and directrix y =…

A: the vertex of the parabola will be at the midpoint of (-3,4) and y=2  That is Vertex= (h,k)=(-3,3)…

Q: Find the equation of parabola with rertex at (0,0 and focus at (3

A: Given the vertex is at(0,0) and focus (3, 0)

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

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Q: Determine the area of the largest circle that can be enclosed by the two hyperbolae, xy= 1 and xy =…

A: Solution is here

Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

Q: Write an equation for the hyperbola which has foci at (0, v5) and (0,-V5 and asymptotes at y = ±3x.

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Q: length of the latus rectum of a hyperbola is equal to 18 and the di equation of the curve if the…

A: The length of the latus rectum = 18,  The distance between the foci = 12,  We have to find the…

Q: Find an equation of the hyperbola that has foci at (0, -10) and (0, 10), and asymptotes y = 1 x and…

A: To find the equation of hyperbola

Q: 3. Find an equation of the hyperbola having foci at (4, 3-V 52) and (4, 3 +/52) and asymptotes at y=…

A: Focii: (4, 3+52) & (4, 3-52)Assymptotes : y=3x2-3 , y=-3x2+9Let vertex by represented by (h,k)…

Q: Find an equation of the hyperbola that has fodi at (-15,0) and (15, 0), and asymptotes y=x and y =

A: here we have to find the equation of hyperbola that has foci  at (-15,0) and (15,0) asymptotes…

Q: Find an equation of the hyperbola (in general form) given the following conditions: 11. C(2, 5),…

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Q: Find an equation of the parabola in standard form with focus at (3,0) and directrix x=-3

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Q: Find an equation of the hyperbola that has foci at (-10,0) and (10,0) , and asymptotes y=3x and…

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Q: 1. Parabolas with axis parallel to the x-axis with focal distance “a" fixed.

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Q: 8. Find the equation of the parabola with vertex at (0, 5) and passing through the point (4,3)…

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Q: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

A: Find the standard form of the equation of the hyperbola satisfying the given conditions as End point…

Q: Find a Cartesian equation for the hyperbola centered at the origin that has a focus at (3, 0) and…

A: The focus is 3,0 c,0=3,0∴c=3 Also the directrix x=ae=1                           ∴a=e Now…

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: 21 Find the equation for the parabola that has its focus at the 2 and has 4 11 directrix at æ = 4…

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Q: Find the eccentricity of a hyperbola having distance between foci equal to 18 and the distance…

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

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Q: Find the equation of the hyperbola that is centered at (0,0), has vertices at (t10,0) and has 6.…

A: Consider the given values. Center=0,0vertices=±10,0y=±65x The gerneral equation of hyperbola with…

Q: Find the standard form equation for a hyperbola with vertices at (0, 2) and (0, – 2) and 1 asymptote…

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Q: Determine the eccentricity of a hyperbola with a horizontal transverse axis of length 24 units and…

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Q: Determine the standard form of equation of a hyperbola with center at (6,4), with a focus at (6, –…

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Q: which satisfies th

A: Parabola: The focus of the parabola is (-2,-5) The directrix x=6 The general form of parabola is…

Q: Find an equation for the hyperbola with foci (0, ±10) and with asymptotes y: = +x.

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Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

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

A: Frist draw a diagram with given information as shown in below figure.

Q: Find the equation of ellipse referred to its major and minor axes as the coordinate axes x, y…

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Q: Find the orthogonal trajectory for the family of parabolas with center at the origin and focion on…

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Q: A hyperbola with asymptotes y = ±2? and y-intercepts (0, ±13). Determine the eccentricity.

A: Consider the given asymptotes y=±2x and y intercept 0, ±13