Find the minimum distance from the point (4, 2) to the parabola y2 = 8x. A 4/3 B) 2/7 © V3 D 2/3

Q: As arch is in the form of parabola with its axis vertical. The arch is 10m high and 5 at the base.…

A: Topic:- application of geometry

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

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

A:

Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

A:

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

A:

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…

A:

Q: Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

A:

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

A:

Q: Find the orthogonal trajectories of family of hyperbola with center at the original and the length…

A:

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

A: Consider the given line

Q: Find the minimum distance from the parabola a – y? = 0 to the point (0, 3). Minimum distance =

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

Q: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

Q: 2. What is the value of y anytime a parabola intersects the x-axis?

A: It is known that the value of y on x-axis is always 0.

Q: -16х2 %3D 0.117 р2 y +2.75х + 3

A: Given, v =  29.97285 y = -16x20.117v2 + 2.75x +3 y at  v =  29.97285 y = -16x20.117(29.97285)2 +…

Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: Find the equation for the parabola that has its vertex at the 1 origin and has directrix at y 41…

A:

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: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

A: We need to find an equation of parabola that intersects the x-axis at (-1, 0) and (3, 0). Thus,…

Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

A:

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

A:

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

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

A:

Q: Find the point on the parabola y = x³ that is closest to the point (1, 2) with two digits accuracy…

A:

Q: A rectangular object 25 m wide is to pass under a parabolic arch that has a width of 32 m at the…

A: The arch can be modeled by the vertex form of a parabola centered at the origin with the base being…

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A:

Q: Find the minimum distance from the curve y = 2 to the point P(6,0)

A:

Q: Find the minimum distance from the parabola x − y2 = 0 to the point (0,3) Minimum distance =

A:

Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

A:

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 minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: What is the minimum vertical distance between the parabola y =x2 +1and y =x -x2 ?

A: Given:

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

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

A:

Q: what is the minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

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

A:

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A:

Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

A:

Q: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

A:

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A: NOTE: Refresh your page if you can't see any equations. . The diameter of the dish is 18 feet and…

Q: Find the length of the arc of the parabola x² 4ay measured from the vertex to one extremity %3D of…

A: We can calculate the length of arc using given condition and  formula of length of arc

Q: What point on the parabola y = 5-x is closest to the point (5,5)? The point on the parabola y = 5- x…

A:

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 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: 19 Find the minimum value of the parabola y = x – 8x +

A: The minimum value of the parabola or any curve is obtained where y' = 0

Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

A:

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

A: Solution is here