Consider the line y = ax , where a is a positive constant. What should be the x- coordinate of the point on the line closest to the point (a, 0) ? a2+a (b). a-a? a? a (a) a2+1 (c). a²+1 a2+1 a2+1

Q: 2. Find the equation of the line (a). Through (1,3) with m = -2; (b). x-intercept -2, y-intercept 4;…

A: we know that equation of line is :  y - y1 = m ( x - x1 )

Q: Find an equation for the line perpendicular to the line −3x−3y=−4−3x−3y=−4 having the same…

A: It is known that, let m1 and m2 be the slope of the perpendicular lines then m1×m2 = –1.

Q: ub-) Find the equation of a line entirely in n which is perpendicular to the line D at the point…

A: You asked to solve part (b) only. So I supposed that you have equation of the plane π and…

Q: Consider the line y = ax , where a is a positive constant. What should be the x- coordinate of the…

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Q: Find an equation of the line that satisfies the given conditions. Throught (2,6); perpendicular to…

A: y=1;(2,6)

Q: (1) What is the relationship between the lines L1 and L2? where ) L1:x = 1-t, y = 4 +t, z = 2+3t…

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Q: Find the point of intersection of the lines with the given equations. 6x + 4y = −10   and   6x + 9y…

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Q: Find the closure of a straight line in R x R_.

A: Given: Straight line in ℝ×ℝ. To find: Closure of straight line in ℝ×ℝ.

Q: Find the distance d between the point M(5, 2, 4) and the line x- 8 y -2 Z-2 %D -8 -9 7.

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Q: The temperature of a rectangular plate bounded by the lines x = ±1, y = ±1, is given by T = 2x2 −…

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Q: In the equation of the line                      ⟨x, y, z⟩ = ⟨x0, y0, z0⟩ + t⟨x1 - x0, y1 - y0, z1 -…

A: The given equation for the line is,

Q: For Exercise, find the slope of the secant line pictured in red (1, 6) y = f(x), (5, 2)A -3-2-! 4 $

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Q: Consider the line y = ax, where a is a positive constant. What should be the x- coordinate of the…

A:

Q: Find the equation of the line that intersects the lines 2x + y – 1= 0 = x – 2y + 3z 3x – y + z + 2 =…

A: We have to find the equation of the line that intersects the given lines and parallel to the line…

Q: Consider the line 3x – 2y = 7. What are the coordinates of the y-intercept for this line?

A: Consider the given equation of the line. 3x - 2y =7 At y intercept, x coordinate is zero.

Q: Find an equation of the tange line to the graph of the equation at the given point. y =2x2+4x;…

A: We have to find

Q: For what values of a and b is the line 2x +y= b tangent to the curve y = ax' when x = -5? a = b =…

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Q: Consider the line y = ax , where a is a positive constant. What is the shortest distance between the…

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Q: Thus, to find the slope of the secant line passing through P(2, 4) and Q(3, 3.), substitute x for x…

A: Topic:- Coordinate Geometry

Q: Find the equation of the line perpendicular to the lines x-1 x+1 쯤 and 1 and 2 == 2-1 2 2 4 3 = y-1…

A: (x-1)/2 = (y-1)/2 = (z-3)/2  And (x+1)/4 =y/3 =(z-1).

Q: Find the equation of a line perpendicular to y=−x−1 that contains the point (1,2).

A: We have to find the equation

Q: Show that if a, b≠0, then the line with x-intercept x = a and y-intercept y = b has equation…

A: Given: x-intercept=ay-intercept=ba, b≠0 To Find:  To show the equation of the given line isxa+yb=1

Q: 2. Find the line L passes through the point (-2,2) a L:2x+y=4.

A:

Q: The line y = kr + 4, where k is a constant, is graphed in the xy-plane. If the line contains the…

A: Given line is: y = kx + 4 ................... (1) The line contains the point (c, d). Then (c, d)…

Q: Show that the equation of the line in R² can be written as х det 1 X1 У1 X2 У2.

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Q: Determine whether there exists a constant c such that the line ex - 2y = 4:  (a) Has slope 4…

A: a) We write the line in the y=mx+b form first  Given that slope=c/2=4  So, c=8  Answer(a): Yes, c=8…

Q: At what points on the curve x=3t^2 + 1, y=t^3 -1 does the ranger line have a slope 1/2?

A: The slope of the tangent line is given by, dydx=dydtdxdt=ddt3t2+1ddtt3-1=6t3t2=2t Given that the…

Q: The slope of the line defined by y – 2 x = 5 is O A. 1/4 О в. -1/2 O C. -2 O D. 2

A:

Q: Consider the line y = ax, where a is a positive constant. What is the shortest distance between the…

A: Given:- Consider the line y = ax, where a is a positive constant. To find:- What is the shortest…

Q: B - Find the equation of the curve whose slope at any point p(x.y) is m = x(x+5)?, and passing…

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Q: Show that the line with intercepts (a, 0) and (0, b) has the following equation. x/a + y/b = 1, a ≠…

A: The two points are given as , a,0 and 0,b. To find the line with intercepts on given points.…

Q: (1) What is the relationship between the lines L1 and L2? where L:x = 1-t, y = 4 + t, z = 2+3t L2:x…

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Q: Find equations of a line perpendicular to the lines x = y = z and x = 2y = 3z, passing through the…

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Q: 12. For the two non-parallel straight lines L:2x- 5y+ 21 = 0 and L: 3x+y+6 = 0, find the coordinates…

A: Consider the following: Line-1:  2x−5y+21=0Line-2:     3x+y+6=0 At intersection point: L1=L2…

Q: Let A(x,y) be the point on the line y = x + 1 that is closest to the point B(2,0). Then the square…

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Q: 8+ (1,2) -8 y= 2x -8-

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Q: The point-slope form of a line is y+y₁ = m(x + x₁), where mis the slope and (x₁, y₁) is a point on…

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Q: For what values of c is there a straight line that intersects the curve y = x' + cx' + 12x² – 5x + 2…

A: Given the equation of a curve , y=x4+cx3+12x2-5x+2. To find the value of c such that there is a…

Q: Consider the line y ax, where a is a positive constant. What should be the x- coordinate of the…

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Q: 14) Identify the point slope form of the line below. A) y - 3-+ 1) B) y+3-1) C) y+3=-+1) y-3D E) y -…

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Q: Determine the value of A so that the line whose equation is Ax+y−7=0 is perpendicular to the line…

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Q: Find an equation of the line that satisfies the given conditions. y intercept 6; parallel to the…

A: y-intercept of the line is 6 and is parallel to the line 2x+3y+4=0. Now the slope of the line…

Q: Consider the line y = ax , where a is a positive constant. What should be the x- coordinate of the…

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Q: Consider the points P(1,0,3) and Q(5, 2, -1), and the line 1: { x = -7-2t y=t z = 9+t

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Q: a) Find the equation of the straight line (y=mx+c) satisfying the given conditions:      i) Passes…

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Q: 4 Adjust the equation so the line passes through the points.

A: Given:   according to  graph dotted point will be 4,2 so, we have two points on line as 0,0,4,2.…

Q: parallel to the line 2x+3y+4=0

A: Equation of line passing through point and with slope m . (y-y1)=m(x-x1)  if two lines are parallel…

Q: Consider the line y = ax , where a is a positive constant. What is the shortest distance between the…

A: Here we use the general formula for calculating the shortest distance between line and point.