Sketch the two families of hyperbolas, the curves xy = k, for various real k and the curves x2 – y2 = m, for various real m. %3D Also show that these two families are orthogonal to each other at any point of intersection of a curve from one family with a curve from the other family. Here we avoid the origin, where there is a degeneracy. Also sketch the families on one graph.

Q: Find a function whose graph is the lower half of the hyperboloid -x2 - y2 + z2 = 1.

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Q: Use the Difference Quotient to evaluate the slope of the tangent line to the first parabola found in…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: 9. Sketch the parabola y =-x +8x-12, show all the intercepts, the axis symmetry and the vertex

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Q: 4. Which line is the horizontal asymptote for the hyperbola y = 6/ ( x - 5 ) + 9 y = 9 X = 5 y= -6/5

A: given,     the parabola y=6x-5+9

Q: What is the families of the curve of all Parabolas with symmetric axis parallel to the y-axis and…

A: Given: What is the families of the curve of all Parabolas with symmetric axis parallel to the y-axis…

Q: What is the general equation of a parabola that opens upward with V(-1,2)?

A: The general equation of the parabola opening upwards is x-h2=4py-k where (h,k) is vertex. here…

Q: The parabola y=(x-)+1 has its fous at (2-3). 76 Determine and State of the the equation directiex.

A: Consider the equation of parabola: y=-116x-22+1To   solve,y-1=-116x-22x-22=-16y-1…

Q: What is the family of curves for all parabolas with axes parallel to the y-axis.

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Q: 1. Find the equation of the curve passing through the focus of the parabola (opens downward and…

A: Given that parabola is passing through (3,0) (1,-1/2). (4,-1/8)

Q: Find the equation of the line that is tangent to the hyperbola at the given point. Write your answer…

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Q: Use your graphing calculator to graph y = ax2 for a = 1 /10, 1/ 5, 1, 5, and 10. Copy all five…

A: y=ax2 when a=110, 15, 1, 5 and 10 The graph when a=110 is, The graph when a=15 is, The graph when…

Q: = 8. Find the equations of both the tangent lines to the hyperbola x² - 4y² 9 that pass through the…

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Q: The parabola y = x^2 is compressed vertically and translated down and right. The point (4, -10) is…

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Q: 17. If the focus of the parabola is (-2, 1) and the directrix has the equation x + y = 3 then the…

A: Given Focus of parabola f (-2, 1) Equation of directrix is x+y =3   Here the objective is to find…

Q: =D1 4 = 1{-5<x<5}

A: Given equation is The equation of given hyperbola is horizontal hyperbola

Q: Identify the vertex of the parabola: Y -5 -7 -4 -3 -2 -1 1 01 90 8 1 2

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Q: Find the equation of the osculating circle of the parabola y= 1 x' at the point where x = 1. Then 4.…

A: The given data is: The equation of a parabola is: y=12x2 To find the equation of the osculating…

Q: Find the slope at the point (1,2) on the graph of the ellipse defined by 4x² + y² = 8.

A: Find slope at the point (1,2) to the ellipse 4x^2+y^2=8

Q: The vertex of the parabola given by the equation x² = 20 y is O A. (0,0) В. (4,5) С. (0,5) D. (4,0)

A: Here we have given that the parabola is x2=20y

Q: Find a parabola with equation y = ax² + bx + c that has slope 10 at x = 1, slope -14 at x = -1, and…

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Q: Find all points where the parabola y = 9 - x² 1 intersects the line y = zx+6. 2

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Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

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Q: o. y = x2 - 4 y-Interoept ( X-Intercept ( ) and (, )

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Q: 4. The accounting department at Factory Shoe has determined that the quadratic relation P = - 2x²+…

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Q: Q,9. What point on the parabola y = v2x + 5 comes closest to the ori

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Q: 3. Families of ellipses whose semi-major axis is twice of the semi-minor axis, vertex at origin.

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Q: O y = -(x+ 4)² + 5 | O y = -(x- 4)² – 5 | O y = #(x – 4)² + 5 O y = -( - 4)² + 5

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