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

Q: Find equations for the asymptotes to the hyperbola described by 49x² – 25y² – 294x – 100y : 884.

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Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

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Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

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Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a…

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Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: 5. Determine the equation of a hyperbola having vertices ( 0,±4) and asymptotes y ±2x

A: Compairing with the given information we have

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: Find the equation for the parabola that has its focus at the (−394,−4) and has directrix at x=−25/4

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Q: Write the equation for the hyperbola with foci (1,-5), (9.-5) and conjugate axis of length 6. (x-…

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Q: 5 Find an equation of the hyperbola having foci at (-2, - 3-/29) and (-2, – 3+ /29) and asymptotes…

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Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: Given: A point moves on the parabola 10y=5x2+3, when x=6 the abscissa is increasing at the rate of 2…

Q: Find an equation of the ellipse with foci at (−3,7)and (−3,−3) and whose major axis has length 20.…

A: The foci of the ellipse is (−3,7)and (−3,−3). The length of the major axis is 20.

Q: What is the equation of the hyperbola with asmptotes y=+-2/5x and a vertex of 0,2

A: The given problem is solved below in detail.

Q: Find the asymptodes of Hx)= x²- 5x+6 the funchion given below X-2

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Q: The hyperbola with asymptotes having the equations y -x and y--x and one verlex at (2, 0) has the…

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Q: Find the equation of the tangent to the hyperbola x2 - 4y2 = 9 at (5, 2).

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Q: Find an equation for the parabola with vertex V(0, 0) and Focus F(0, 2), and sketch its graph.

A: We have given vertex V0,0 and focus F0,2. Given the vertex of the parabola is V0,0 and focus is at…

Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

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

A: It is given that the Vertex is V(0, 0) The focus is on the positive x axis, 2 units away from the…

Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

A: We need to find an equation of parabola that intersects the x-axis at (-1, 0) and (3, 0). Thus,…

Q: Find the equation of the parabola with vertex V (5,5) and directix the y-axis.

A: we have to find the equation of parabola

Q: Find an equation of the ellipse with foci at (-4, 3) and (-4, –9) and whose major axis has length…

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Q: Find an equation of the hyperbola having foci at (1,-2-/25) and (1, -2+25) and asymptotes at 3 r- 4.…

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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 the equation for the parabola that has its vertex at the origin and has directrix at x=−1/28..

A: The standard form of equation of parabola with horizontal axis is given by the formula, y2=4px…

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

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Q: Find the standard form equation for a hyperbola with vertices at (0, 3) and (0, – 3) and asymptote y…

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Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: Find the asymptotes of the hyperbola 3x2 + 6x − y2 − 10y = 1.

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Q: Find an equation of the tangent line to the hyperbola defined by 5x^(2)+4xy−2y^(2)−4x=19 at the…

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Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

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Q: Which is the corresponding equation of the hyperbola with foci located at (-8, 0) and (8, 0) and a…

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

A: equation of parabola  (x - h)2 = 4p (y - k) where (h,k)=(0,0) vertex ordinates directrix y=3 , y= k…

Q: The asymptote of the hyperbola given by x²/9- y²/4 = 1 has the equation?

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Q: Find an equation of the ellipse with foci at (-5,9) and (-5,-10) and whose major axis has length 22.…

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Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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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: Write the equation for the hyperbola with foci (1,-s), (2.-s) and conjugate axis of length 6. (x-…

A: Please refer the attached image for complete solution.

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

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

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Q: 1 Find an equation of the hyperbola having foci at (5-/45, 0) and (5+/45, 0) and asymptotes at y = 5…

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Q: Find the point(s) on the ellipse 4x² + y² = 4 that are farthest from the point (1,0).

A: We need to find the points on the ellipse that is farthest from the given point. According to first…