What is the length of the minor axis given by the equation (x+2)^2/4 + (y−1)^2/16 = 1 ?

Q: Suppose you start at the origin, move along the x-axis a distance of 7 units in the positive…

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Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

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Q: What is the equation of a line parallel to 킹 =Dz+ 2 that passes through (1, 2)?

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Q: What is the distance between the line with Cartesian equation x-6 = y-1 =z and the line with…

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Q: the distance from the point (5,3) to the line 2x+4y+5=0 is

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Q: A straight conncecting street segment is built perpendicular to an existing street with equation y =…

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Q: Find the point on the line 4x + y = 7 that is closest to the point  (−4, 2).

A: Let P(x,y) be the point on 4x+y=7 y=7-4x Distance   D2=x+42+y-22Z=x+42+7-4x-22Z=x+42+5-4x2

Q: Find an equation of the line through the point (3, 2) that is parallel to the line 2x +y +5 = 0.

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Q: Find a point on the line 3x − y = 4 that is closest to the point (–2, 3)

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Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (3,2v3).

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Q: What is the x-coordinate of the x-intercept of the line 2 = 1 when it is graphed in 3 5 with…

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Q: Find the point on y – axis which is equidistant from the points (3, 1, 2) and (5, 5, 2)

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Q: Find the point on the line 6x + y = 6 that is closest to the point (-4, 1). (x, y) = %3D

A: We have to find a point on the line 6x + y = 6 that is closest to the point (-4,1). Concept Used -…

Q: Find the equation for a quadratic with vertex at (-4, 4) and y-intercept at (0, 1) y =

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Q: What is the equation of a line parallel to the line y=2x that passes through the point (0,4)?

A: Solution:      Equation of any parallel line to y = 2x is      y = 2x + c where c is constant.

Q: How to find an equation of the line tangent to the circle x^2+y^2-6x-2y-15=0 at the point (6,5) ?

A: Note:- The standard form of equation of tangent line at point c, d is y-d = m x-c Here, m is the…

Q: There is a line through the origin that divides the region bounded by the parabola y and the x-axis…

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

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Q: opens upward with vertex at (-12,-6) with directrix y=- 17

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Q: Find the'equation of the line that is perpendicular to y = -2x + 1 and contains the point (8, 2). =…

A: We are given the line y = -2x+1. And the slope of the above line is -2. So, the slope of the line…

Q: What is he symmetric equation of the line that passes through the points (3, 0, 11) and (2, 6, 7)?

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Q: Pam walks along a road which can be modeled by the equation y 3x, where (0, 0) represents her…

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Q: What is the distance between the line with Cartesian equation x-2 = y-8 = z-3 and the line with…

A: If first equation of the line parallel to the vector V1 through the point P1 and the second equation…

Q: Find the distance between the points (-3,0) and (3,1)

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Q: Find the equation of a line perpendicular to −4x+y=−5 that contains the point (−5,1).

A: We have to find the line perpendicular to y=4x-5 and passing through (-5,1)

Q: The distance from the point (2,1) to the line  4x-3y+5=0 is

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Q: Find an equation of the line passing through the point (2,1) that is perpendicular to the line…

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Q: Find an equation of the diameter of circle x²+y²-6x+2y-15=0 which when produced passes through the…

A: Given, Equation of the circle x2 +y2 -6x+2y-15 =0  We have to find the equation of the diameter of…

Q: The point that is symmetric with respect to the y-axis to the point ( - 2, 5) is__________

A: It is known that the graph of y=fx is symmetric with respect to y-axis means f-x=fx=y.

Q: Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope is (-1)? If so, find tangent and…

A: Given:  The equation of a parabola y=2x2-13x+5. We have to find whether the parabola have a tangent…

Q: What is an equation of the line that passes through the point (4, –3) and is perpendicular to the…

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Q: Find the coordinates of the point other than the origin where the equation x3 + y3 - 72xy = 0 has a…

A: W we have to solve

Q: What is the distance between the line with Cartesian equation x-1 = y-6 = z and the line with…

A: Given:- The line with cartesian equation x-1=y-6=z and the line with the cartesian equation…

Q: Find the point on the line y = 2x + 3 that is closest to theorigin.

A: Given equation of line,  y = 2x + 3 To find the point on line that is closest to the origin.

Q: What are the coordinates of point of intersection of y=x+3 and y=3x-3?

A: Equating y = x+3 and, y = 3x-3, we get, x+3 = 3x-3 So, 2x = 6 So, x = 3

Q: What is the coordinates of the point on the line y = 2x +1 which is closest to the point (2, 1)?

A: The point on the line y=2x+1 which is closest to point (2, 1) is the point through which a line…

Q: Find the point P on the line y=6x that is closest to the point (74,0).  Type an ordered pair.

A: Given:The line y = 6x and a point (74,0).Let p be the point that is closest to the point (74,0). Let…

Q: What is the distance between the line with Cartesian equation x-2 = y-7 = z and the line with…

A: Consider the line, l1=x-21=y-71=z1  and    l2=x-71=y-71=z-11 The formula for finding shortest…

Q: Find the point on the line 6x + y = 7 that is closest to the point (−4, 2).  (x,y)=

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Q: Write the equation of the circle of radius 5 that istangent to both axes and passes through the…

A: Write the equation of the circle of radius 5 that istangent to both axes and passes through the…

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

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Q: What is the equation of tangent to the parabola y^2 = 2x + 8 at (4,4) ?

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Q: What is the distance between the line with Cartesian equation x-1 = y-6 = z and the line with…

A: Explained below

Q: What is the equation of a circle passing through (6,2) and tangent to the line x-4y-15=0 at (3,-3)?…

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Q: Find the distance of the point (2, 6, 4)  from the x-axis by two methods

A: To find the distance between the point.

Q: Find the distance between line 3x + 4y = 10 and point (-2, -1/2)

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Q: What is the distance between the point (-2, 5, 3) and the z-axis?

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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.