Consider the diagram below in a two dimensional Cartesian x-y plane. The parabola is given by the equation y = kx² where k is a positive constant. The circle of radius r 'sits' on top of the parabola, i.e. the circle touches the parabola at two points. Determine c, which is the distance of the centre of the circle from the x-axis, in terms of k and r. circle o parabola x-axis

Q: 3. One point on a parabola is (-9, 11). The focus of the parabola is (3, 2). 1) Write the equation…

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Q: Find the vertex, focus and directrix of the parabola given by (x - 2)2 = 4(y + 1)..Then graph the…

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Q: Eliminate the arbitrary constants. Parabolas with x-axis parallel to the x-axis.

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Q: Calculate the focus and the directrix of the parabola x^2 + 2 x y + y^2 - 4 x + 2 y - 6 = 0.

A: The given equation of conic is:To find:The focus and directrix of the given parabola.Concept:The…

Q: One point on a parabola is (–7, 17). The focus of the parabola is (5, 1). Which equation represents…

A: Given

Q: Determine the focus of the parabola (x - 2)² = 4(y - 3). %3D O (-1,-3) O (2,4) O (-2,-2) O (2,3)

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Q: Please don't provide handwritten solution...

A: Explanation is given below:Explanation:Given equation: 5y−x2=20 Rewrite it in the standard form of a…

Q: If the axis of symmetry of a parabola is given by x = 4, is it possible for the directrix to have…

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Q: Find the Parabola with Focus (7,-2) and Directrix x=-9

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Q: Determine another point on each parabola. The axis of symmetry is x = 3. A point on the parabola is…

A: The axis of symmetry of a parabola is a line about which the parabola is symmetrical.

Q: Which equation would shift the parabola down 3 units? A y=z² B y=z² +3 C_y=(z-3)² Dy=(z+3)²³ E =…

A: which equation would shift the parabola down to 3 units.

Q: 3. All vertical parabolas. Ans: y" = 0

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Q: The equation of the directrix of a parabola is y = 5 and its focus is at (4,-7). What is the length…

A: given:Equation of direction of a parabola  is y=5focus 4,-7To calculate: length of latus rectum

Q: Verify that the mapping z + z², (z e C) will map the line y = -3 to a parabola. Find its Cartesian…

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Q: Define the term parabola?

A: Given: The term parabola.

Q: 3. Complete the table for each parabola Equation Y= -0.4(x-2)2 Y = 3(x + 5) 2 + 3 Direction of…

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Q: 3. Write the equation of the parabola that matches each description. a) The graph of y =x² is…

A: 3. According to questionGiven Curve :y = x2

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.