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

Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

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

A:

Q: Find the exact length of the curve. y = 4 + 2x3/2, 0 < x < 1

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: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

Q: Please

A: Now differentiate it with respect to y and equate it to 0.

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: 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: 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 the exact length of the curve. y = 4 + 6x3/2, 0 < x < 1

A:

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

A:

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: Find the vertex of the given parabola. Give all values correct to 3 decimal places. y = 7x2 - 8x +…

A: A detailed solution is given below

Q: Find the exact length of the curve.y = 4 + 2x3/2, 0 ≤ x ≤ 1

A: Please see the white board for the formua to calculate the length, L of the curve y = f(x), over the…

Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

Q: Find the shortest distance from the point (1,4) to a point on the parabola y =2 x (a) /2 (b) 1 (c) 2…

A: To determine the shortest distance between point and the parabola,

Q: Find a point on the parabola y - x* + 9 which is closest to the origin.

A:

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

A:

Q: find the points on the parabola y=x^2 closest to the point (0,1)

A:

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 point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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

A:

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

A:

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

A:

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

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

A:

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

A:

Q: Q,9. What point on the parabola y = v2x + 5 comes closest to the ori

A:

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 2.

A:

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

A:

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…

A:

Q: i) Find the exact length of the curve y=+15x52 4x3 1 ≤ x ≤ 2,

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

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 d faumthe point to the plane X+y+Z=8.

A: Let's find.

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

A:

Q: If P(a, a²) is any point on the parabola y = x², except for the origin, let Q be the point where the…

A: To Determine: If P(a,a2)is any point on the parabola y=x2,except for the origin,let Q be the point…

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