Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

Q: Find the abscissa of the point on the graph of y=V 2x – 1 that is parallel to the line 2x - y+1=0

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Q: Find the point (x0, y0) on the line 4x + 9y = 12 that is closest tothe origin.

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Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.

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Q: Find the slope of the line tangent to the graph of x^2+2xy^2+3y=31 at the point(2,-3)

A: The slope of the tangent line can be calculated by using the derivative of the function at the point…

Q: find the slope of the line tangent to the curve x2=y2+3/2xy at (4,2)

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Q: Explain the steps required to find the length of a curve y = ƒ1x2 between x = a and x = b.

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Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: Find equations for two lines that are both tangent to the curve y = x³ – 3x² + 3x – 3 and parallel…

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Q: Perpendicular to y + x = 0; (2, 0) on line

A: To find equation of a line ,which is perpendicular to line y+x=0,and point (2,0) lies on line.…

Q: Find the equations for all the lines tangent to x + y° – y= 1 at x = 1. r+ y³ – y = 1 2

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Q: Find the equation of the line segment tangent to the curve y−2x2−1=0y−2x2−1=0 which is parallel to…

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Q: The equation of the line tangent to the curve y=3x+4/4x-3 at the point (1,7) is  a) y - 25x=-18 b) y…

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Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

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Q: Find the equation of the line segment tangent to the curve y−2x^2−1=0 which is parallel to the line…

A: Given curve is y-2x2-1 = 0

Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: Find equations of both lines through the point (2, - 3) that are tangent to the parabola y = x2  + x…

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Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

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Q: Where does the line x = 1 + t, y = 3−t, z = 2t intersect the cylinder x² + y² = 16?

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Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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Q: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: Find the equation of the line tangent to 3x²y + 4xy2 = 6x² + 5y at the point (1,).

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Find the equation of the line tangent to y = x2 - 1 going through x = 1

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Q: Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

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Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: Find equations for two lines through the origin that are tangent to the ellipse x2 – 8x + y² + 3 =…

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Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

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Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

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Q: Find the equation of the line tangent to the ellipse x^2 - xy + 2y^2 - 4x + 2y + 2 = 0 if the…

A: given equation of ellipse x2-xy+2y2-4x+2y+2=0 and a line  4y-x+2=0 to find equation of line tangent…

Q: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: Find the equation of the line tangent to the parabola y = x^2 -1 at the point (-2,3).

A: Given the parabola :

Q: Find the equation of line passing through (5, 8) and perpendicular to y - axis. Oy = 5 Oy= 3 Ov=0 Oy…

A: The general equation of the straight line is: y=mx+c Now, the slope of the y-axis is infinity. So,…

Q: Find the equation of the line normal to x^3 + y^3 = 6xy at (3,3)

A: Given, x3+y3=6xy

Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

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Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: The x coordinate of the point of intersection between the two curves 12x y = = el2# and y = 1 is x =

A: Our Aim is to find the x coordinate of the points of intersectionbetween the two curves y=e12x and…

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,

Q: The equation of the line that is tangent to the curve y=2x3−6x and is perpendicular to 18y+x+3=0…

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Q: Find an equation of the line tangent to the curve y = v4x – 3 – 1 and perpendicular to the line x +…

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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.