If the intersection points of the hyperbola 3x² – y² = 11 and the line 2x + y = 10 are P and Q, which of the following is the midpoint of [PQ]? A) (20,30) B) (20,-30) C) (-20,30) D) (18,-24) E) (18,-30)

Q: 1. Given the equation that describes 1 y=-(x-2)² +27, determine: a) the vertex b) the domain and…

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Q: y = 2(x+3)2 %3D y = 4(x+3)² For the quadratic equations shown here, which statement is true? A) The…

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Q: What is the vertex of the parabola y=(x+3)²-4? A (3,4) B (-3,4)

A: The vertex of standard parabola equation  y = x2  is at (0,0)

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

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Q: Find the midpoint of these two sets of points; (2, -5) & (-3, -10).

A: Given: The two sets of points are (2, -5) and (-3, -10)

Q: The plane through the points (-4,-8,-1), (8,3,5), (7,8,6) has equation Ax + By + Cz= D. If A = - 19…

A: Since plane passes through the given points therefore

Q: iv) y=-x- 3 1 v) y=-2x+ vi) y=;* 1 21 y y y 1 =-2.5 1 2 2 y y y 2 2 2 -2 -2 -2 2 -2 2 2 y-intercept:…

A: We have to write equation in the form x/a+y/b=1 for y-intercept , here b is y-intercept

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

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Q: the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axes at concyclic points,then prove that…

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Q: 23. (LO13) From the graph of the parabola, determine the axis of symmetry. Ay A) Axis of Symmetry:…

A: answer is x=-a   explanation is given in below step

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: 9. Each pall of points is located on opposite sides of the same parabola. Determine the equation of…

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Q: Write an equation for the parabola whose vertex is at (3, 6 ) and which passes through point (4, 4…

A: Given Data: The vertex of the parabola is: (h, k)=(3, 6) The coordinate of a point on the parabola…

Q: 5. a) Match the table to the equation. A. y В. y с. y -1 1 -2 -7 3 1 5 -1 -5 1 1 7 1 -1 i) y= 2x –…

A: For equation y=mx+c m-represent the slope of line. c represent the y-intercept. a. We can see from…

Q: Which of the following equations represents the parabola

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Q: 12. Expand and simplify. (5x + 3y)²-(4x + y) (6y - x) 13. The formula V = nr³h represents the volume…

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Q: Convert the following. form to general form of parabola a₁)(x-3) ²= 12 (1-4) 6.)(x-1)² = 8(4-3)…

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Q: 1. Find an equation of the perpendicular bisector of the segment joining(3. -1) and (-1. 7). (A) x +…

A: Here we have to find the equation of line which is perpendicular bisector of the segment joining(3.…

Q: 9. The endpoints of the latus rectum of the parabola (y + 2)2 A. (-1,0) and (-1,–4) B. (1,0) and (1,…

A: A lotuc rectum of a parabola isbthe chord that passes through the focus,is perpendicular to the…

Q: Find the distance between each pair of points: a) (0, - 3) and (4, 0) c) (3, 2) and (5, - 2) b) (-2,…

A: Distance between two points x1, y1  and x2, y2 is  d = x1 - x22 + y1-y22  a) (0, -3) and (4, 0) d =…

Q: 11) Determine the equation of the line parallel to y - 57 = -4(x + 58) that contains the point (95,…

A: Question number 11,Given,        The equation of the line parallel to y-57=-4x+58 that contains the…

Q: If the lines a₁x + b₁y+C₁ = 0 and a₂x + b₂y + C₂ = 0 cut the coordinate axes at concyclic points,…

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Q: 1. Given: (x - 5)² = -20(y + 7); what is the vertex? A) (-5, -7) O A OB O O D B) (-5, 7) C) (5, -7)…

A: Find the vertex of the given parabola

Q: 2) The distance between two points with coordinates (x₁, y₁) and (x2, y2) is equal to √(x₂-x₂)² +…

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Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: 10. Which equation represents the parabola that has been vertically stretched by a factor of 5,…

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Q: Find the distance between each pair of points: с) (-4, 1) and (4, 5) d) (x — 2, у —3) and (х + 4, у…

A: Distance between two points Ax1, y1 and Bx2, y2 is, AB=x2-x12+y2-y12

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.