Determine the value(s) of k such that the circle x²+(y-6)²=36 and the parabola x²=4ky will intersect only at the origin

Q: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: At what point does the line normal to the graph of y=5−4x+4x2 at (1,5) intersect the parabola a…

A: The given function is- y=5-4x+4x2.................1 Differentiating the above expression w.r.t. x-…

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

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Q: Find the x-intercepts and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If there…

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Q: Let P and Q be distinct points on the parabola y = 2r such that a circle with PQ as diameter passes…

A: The given equation of parabola y2=2x Let P and Q be points on the parabola  Parametric coordinates…

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: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Identify the quadric surface and sketch the graph. z = x2 + 4y2

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Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

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

A: equation of parabola:-

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: 1. Transform the general equation of the circle x² + y² + 8x - 2y - 8 =0 into its standard form and…

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

A: Given:Vertex=0,0Directrix y=-3Equation of parabola:x-h2=4py-k

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

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Q: 5. Determine the value(s) of k such that the circle x² + (y – 6)² = 36 and the parabola r? = 4ky…

A: we have to find the value of k. the solution is following.

Q: A] Find the length of the arc of the semi-cubical parabola y² = x3 (1,1) and (5,5V5). between the…

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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: A rectangle is inscribed in the parabola y=8– x - such that one side lies on the x-axis and two…

A: Answer

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

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: Find the length of the arc of the semicubical parabola x  sq = ycu . betweenthe points (2,2 )  ; (4,…

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Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

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Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2 Ans: 2xy" - 4yy"…

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

A: find the equation of a parabola vertex=(0,0) and directrix x=-4

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

A: Here we find the equation of parabola.

Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: A parabola with a negative latus rectum has endpoints at (5, 1) and (5, -11) Where is the vertex? *

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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: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

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: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

Q: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

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

A: Given query is to find the equation of the paraola.

Q: Concentric with the circle x ^ 2 + y ^ 2 - 4x + 6y - 17 = 0 and 3x - 4y + 7 = 0 equation of the…

A: Solution:- x2+y2-4x+6y-17=0 x2-4x+6y+y2=17 x2-4x+4+6y+y2+9=17+4+9 x-22+y+32=30 Center of circle (2,…

Q: True or False Every equation of the formx2 + y2 + ax + by + c = 0 has a circle as its graph.

A: The given statement is,  Every equation of the form x2+y2+ax+by+c=0 has a circle as its graph. To…

Q: Determine the coordinates of points A and B on a parabola y midpoint of AB is as close as possible…

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Q: 1. Determine the equation of the parabola whose vertex is at the point (-1, –1) and whose directrix…

A: We have to determine the equation of the parabola whose vertex is at the point (-1,-1) and whose…

Q: What point on the parabola y = 6 – x is closest to the point (6,6)?

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Q: The graph of y^2 = x^3 is called a semicubical parabola. Determine the constant b so that the line y…

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Q: Find the equation of the parabola that is symmetric about y axis with vertex at the origin and…

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Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: Show that the envelope of the family of circles whose diameters are the double ordinates of the…

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Q: Find the shortest distance of the point (10,4) to the parabola y=x2

A: Consider a  point on parabola  y=x2. Distance of this point with (10,4) s2=(x-10)2+(y-4)2…

Q: Find the x-intercept(s) and the coordinates of the yertex for the parabola y =x´ +4x+4. If there is…

A: The given parabola is: y=x2+4x+4 To find the x-intercept and the coordinate of the vertex for the…

Q: Find an equation for the parabola that has its vertex at the origin and has a directric at x=1/29

A: We want to find out the equation of the parabola.

Q: Find the shortest distance of the point (6,3) to the parabola y=x2

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