Find all points that are on the graph of y=3x2and are closest to the point P(0,5). Enter the exact value(s) of the x-coordinate(s) of all such points. If there are more than one, separate them by a comma. The x-coordinate of the closest point(s):

Q: Find all points on y-axis of the rectangular coordinate system that are a distance 6 from the point…

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Q: Point T (* 0) -2+

A: Graph of the function is given, we have to find the coordinate of the point T.

Q: Find all points on the y-axis that are a distance 6 from P(5,3).

A: A point on the y axis is of the form (0,k) , where k= real number. Let (0,k) is 6 units away from…

Q: Find the distance between the points of intersection of the graphs y = x+2 and y = 4 - x.

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Q: Find all of the possible values of the constant k for which is the equation of a circle. x² + y² +…

A: Solution: x2 +y2 +10x -14y +k2+10 =0 We know the general form equation of circle x2 +y2 +2gx +2fy +C…

Q: Find the midpoint of the following two points (4,8) and (3,7)

A: The two coordinate points  (4,8) and (3,7) We need to find the midpoint of the given two points.

Q: Find all points having a y-coordinate of - 6 whose distancefrom the point (1, 2) is 17.(a) By using…

A: a. Using Pythagorean theorem. The converse of the Pythagorean Theorem states that the sum of the…

Q: Find the slope of the curve Y = Vx at the point P (4, 2).

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Q: Find all the asymptotes of the curve 3x3 2x2y – 7xy? + 2y3 – 14xy+7y² + 4x + 5 = 0 ?

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Q: Find all points having an x-coordinate of 3 whose distance from the point (- 1, - 4) is 5. The…

A: Given point is  (-1,-4). and distance is 5.

Q: List the quadrant or quadrants satisfying the condition : x3 > 0 and y3 < 0

A: The given condition is x3>0 and y3<0.

Q: Find all points having a y-coordinate of - 3 whose distance from the point   (1, 2) is 13.

A: Consider the points are A = (x,-3) and B=(1,2) The distance between A and B is 13 units.   If the…

Q: In the Cartesian plane below, rectangle MNQR is shown. y (cm) N(12,29) M P >x (cm) R • An ant starts…

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Q: Find the extreme values of ƒ(x, y) = x3 + y2 on the circle x2 + y2 = 1.

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Q: Find the coordinates of the points that are 13 units away from the origin and have an x-coordinate…

A: Solution: Find the coordinates of the points that are 13 units away from the origin and have an…

Q: fird the equation of the fangent lineto the graph of Y= ☆ at X=2

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Q: Find the distance between the points p1and P2.

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Q: Find the length of the chord intercepted by the circle x2+y2+3y-22=0 on the line y=x-3

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Q: Find the area of the triangle that lies in the first quadrant (with its base on the x-axis) and that…

A: y=2x-4 and y=-4x+20 We need to find the area of the triangle that lies in the first quadrant (with…

Q: Find the distance between the points p1and P2.

A: Given: P1=-1, 1, P2=2, 2

Q: Ay -2

A: A line is generally an object in geometry that doesn't bend i.e. it has no curve. It is a collection…

Q: Find the point P' symmetric of the point P(-5, 13) with respect to the line 2x - 3y - 3 = 0

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Q: Q2) Find the distance between the line y= - (x+2) & the center of the circle y+x-4(x+ y)= 9

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Q: Q2) Find the distance between the line y= - (x+2 ) & the center of the circle y + x – 4(x+ y )= 9

A: The center of the circle x2+y2-2ax-2by+c=0 is a, b Therefore, the center of the given circle…

Q: Find all points having a y-coordinate of -6 whose distance from the point(1,2) is 17. (a) By using…

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: Find the distance between the points of intersection of the graphs y = x² + 2 and y = 11. %3D

A: Given y = x2+2y = 11

Q: Find the distance from the point (5,8) to the circle x+y2 + 2x + 6y +3 = 0

A: Please see the explanation below

Q: a) Find the Extreme values of f(x, y) = x³ + y² on the circle x² + y² = 1.

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Q: Find the shortest distance from the point (- 1, – 2, 5) to the cone z = x² + y². Please | round to…

A: Distance of a point from cone is                                      d=(x-x1)2+(y-y1)2+(z-z1)2 from…

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given expression for x and y is given by  x = t - 2  and  y = 2t+3 The range of t is 0≤t≤5 t = x…

Q: Q2/ Find the equation of the circle tangent to the lines, y =-2x+3, y = - 2x+7, y-+늘and y- +글 %3D…

A: The lines given by y=-2x+3 and y=-2x+7 will be parallel to each other as they have the same slope m.…

Q: Approximate the point of intersectión of the graphs of r and g. (x, y) = (

A: Given,

Q: Find the points on the curve y 13x closest to the point (0, 5). )and (

A: Topic:- point  on the curve

Q: Q6. Find and classify the stationary points and the points of inflexion on the following curve. y =…

A: Stationary point of a differentiable one variable function: It is a point on the graph where…

Q: Find the distance from the point (4, 3, 0) to the y-axis

A: We have to find the distance from the point 4, 3, 0 to the y-axis. We know that distance from the…

Q: Find all points on the y-axis that are a distance 6 from P(5, 3).

A: P5, 3 is at a distance of 6 units from the y-axis

Q: 8. 3y = x' + 3x? – 9x + 3 %3D

A: Given: y=x33+x2-3x+1 We know that any given functiony=fx have maxima at x=a, if f'a=0 and f'x change…

Q: Use the indicated x-values on the graph of y = f(x) to find the following. y C

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Q: (i) Find the co-ordinates of the points A and B where the line y= 2x- 1 cuts the curve y= x2 – 4.…

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Q: Find the x- and y-coordinates of the point C.

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Q: Find the point in the curve y = x³ + 3x for which y' = y'

A: Roots of y' problem....

Q: B. Find the point on the line y = 10 – 2x that is closest to the origin. REFLECTION

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Q: Find an equation for the set of all points equidistant from the planes y = 3 and y =-1.

A: Find an equation for the set of all points equidistant from the planes y = 3 and y = -1.

Q: Q2) Find the distance between the line (y=x+4) and the center of the circle (y+x-4x-4y%34)

A: A detailed solution is given below.   (As per our guidelines, we have to solve only 1st question)

Q: Q2) A- Find the distance between the line (y = x + 3 ) and center of circle (x²+y²–2x=0).

A: Topic : Coordinate Geometry  Answer  question no 2 :- sqrt(8) As per our guidelines,  at a time only…

Q: Q4: Find the distance from the origin point to the line x-2y-1 %3D

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Q: Evaluate F. dr,where F(x,y)=j and C isthe part of the graphof y = 12x³ – x from (2,2) to (– 2, – 2)

A: Line integral is integral of some function along a curve or path. Any field for which the line…

Q: State the curve domain and coordinates of the point where the curve cross es the n-axis y: In (2x…

A: Given y= ln(2x - 5)  The domain of a function is the complete set of possible values of the…

Q: Suppose the graphs of y = 5x? + 3x + 4 and y = x³ + bæ? – 78x – 158 intersect at x = – 9. Find all…

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Q: Let x + y = 28. Find y"(x) at the point (3, 1). "(3) =

A: The solution of the problem is given in the next steps.

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.