To y=x²-12x + 20 Parabola Wite the intersection point of the tanpent lines drawn from (2,0) and Li0,0) points

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  Vertex: (2/3 ,…

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Q: Find the parabola with equation y=x^2+bx+c that has slope of 8 when x=9 and passes through the…

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

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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: 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: dr if F= and C is a piece of the parabola y=4-x² from the point (–1,3) to the point (2,0).

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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: 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: Consider the parabola y = -x +4x + 9 and the line y=2x + 1. Solve for the x-coordinates at their…

A: x - coordinates of the point of intersection = ?

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: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

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: Find the point on the parabola y* = 2x that is nearest the point (1, 4).

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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: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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Q: Find a parabola with equation y= ax2 + bx +c that hasslope 4 at x=1  , slope -8 at x= -1 , and…

A: The parabola is y=ax2+bx+c. It has a slope of 4 at x=1 and slope of -8 at x=-1 and passes through…

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: 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: Find the tangent line to the parabola x2-6y=10 through (3,5) (ILLUSTRATE SOLUTION)

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Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

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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 the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: Find the point on the parabola y=x^2 that is closest to the point (6,3) what is the distance between…

A: Given: To find the point on the parabola y=x2 that is closest to the point (6,3) what is the…

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: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

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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: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: Find the standard equation of a parabola if its latus rectum measures 9 units, axis at y = 3, p is…

A: Let's find standard equation of a parabola.

Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

Q: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

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Q: Find the point on the parabola x = t, y = t2, -∞ < t < ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x + y² + 5 = 0.

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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.

Q: Find the point on the parabola y=x2 closest to (6,3

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Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

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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 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: Find the x intercept(s) and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If…

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Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

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: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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Q: Find the point P on the parabola y = x2 closest to the point (57, 0). (х, у) %3D ]-«

A: Given the equation of parabolay=x2         ........(1)

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

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Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)

Q: Find the parabola with equation y = ax? + bx whose tangent line at (2, 8), is y = -2x + 12.

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Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.