Find an equation of the line containing the centers of thetwo circles x2 + y2 - 4x + 6y + 4 = 0 and x2 + y2 + 6x + 4y + 9 = 0

Q: Identify the graph of the linear equation 4x + 2y + z = 8 in three dimensional space. (0,0,2) (0,…

A: We need to identify the graph of the function 4x+2y+z=8 We will do so by seeing if the points that…

Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

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

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Q: find the distance from the point to the line. (0, 0, 12); x = 4t, y = -2t, z = 2t

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: Find the point on the line x /a + y/ b = 1 that is closest to the origin.

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Q: Find the line L, that passes through the point P(1,2) and parallel to the line L2: x+2y=3.

A: Given data is: The equation of the line L2: x+2y=3 To find the equation of the line L1 that passes…

Q: 4. Find the equation of the locus of the points P(x, y) whose distances from the point (3,2) are…

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Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: How do I do this?

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Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: a) Find the distance between the point P (9, 1) and the line 3x+4y 6.

A: As per our guidelines we are supposed to solve only one question i.e. the question no (a). For the…

Q: a) Find the distance between the point P=(9, 1) and the line 3x+4y=6.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the maximum and minimum values of the function ƒ(x, y) = 3x + 4y on the circle x2 + y2 = 1.

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Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

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Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

Q: . If a point P is moving such that the lengths of tangents drawn from P to the circles x² + y² +8x…

A:

Q: Find the orthogonal trajectory of the circles x² + y² + ay = 0

A: GIvenx2+y2+ay=0To findorthogonal trajectory of above curve.

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Find the midpoint of points A(-9,7) and B(1, 10) graphically.

A: We will use section formula to find solution to the problem .

Q: Find the center of the circle tangent to x^2 + y^2 + 2x - 6y + 5 = 0 at (1,2) passing through the…

A: First find the equation of the tangent. The point (1,2) is tangent to the given circle. The general…

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

A: The given equation of the line is, y=x+1 Let the point x,x+1 is closest to the point 4,1 Using…

Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

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Q: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

Q: Find an equation of the line which is tangent to the circle z + y - 4x + 6y – 12 = 0 at the point…

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Q: Find the point(s) of intersection of the parabola y =x2+ 2 andthe line y = x + 4.

A: The given functions are y=x2+2   and   y=x+4

Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

Q: Determine shortest distance of the line 2x-3y-8 to the vertex of the curve x2 - 4a 4y +4 0. O 2 O…

A: We have given a line ,and find the shortest distance from vertex of parabola to line.

Q: Find the distance between the point (−3, 1) and the line 4x + 3y + 4 = 0.

A: Given standard equation of line 4x+3y+4=0 and a point (-3,1)

Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Find the latus rectum of the curve 4x2+9y2+8x -32 = 0

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Q: Find the line of intersection of the given planes. 4x + y + z = 0 and 2x -y + 3z = 2

A: Given planes are: 4x + y + z = 0 2x - y + 3z = 0 Let us consider, z = t Then we get, 4x + y = -t 2x…

Q: Find the point where the common point of the circles x2+y2=25 and x2 +y2-12x-6y+35=0 intersects…

A: Here we have to find the point where the common point of the circles x2+y2=25 and x2 +y2-12x-6y+35=0…

Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: Write the equation of the locus of a point whose distance from the plane 3x-2y-6z=12 is always twic…

A: We have to find the locus of the point P with the relation as per the distances given.

Q: Find the line of intersection of the planes 2x – y + z = 2 and x + 2y – 4z = 1

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Q: show that the curves 6x^2-5x+2y=0 and 4x^2+8y^2=3 touch each other at (1/2,1/2)

A: To find :                   The curves touch each other  Let                       6x2 - 5x + 2y = 0…

Q: Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2)

A: Given that: Line is: y=5x+7and collineation is: (x, y)=(2y-x, x-2)

Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: What are the coordinates of the center of the curve x2 + y2 – 2x – 4y – 31 = 0?

A: Given, To find coordinates of center for the curve x2 + y2 – 2x – 4y – 31 = 0?

Q: show.. that. the line in.which. and. .5Xm2y.Z==.0. jntersect..is

A: Equation of the plane: - In three-dimensional space, a plane surface is represented by an equation…

Q: Find the exac length of the curve 3/2 , 0dxE y=2+2x

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Q: Find the point on the line x + 2y = 5 that is closest to the origin.

A: Let the point (x, y) on the given line x+2y=5  is closest to the origin (0, 0). observe that…

Q: Find the distance from the point P(-1,3,-5) to the plane through the three points Q(3, 1, -3). R(4,…

A: The points passing through the plane are: Q3, 1, -3R4, 6, -5S5, -4, -6

Q: Find the distance between the plances 3x + y - 4z = 2 and 3x + y – 4z = 24

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Q: Find the locus of the points that are equidistant to the point F (0,2) and the line y=-2

A: Use distant formula..

Q: Sketch the graph of the following quadratic surfaces a) 4x² +9y² + z² = 36 b) x² - y²z² = 1 c) x²…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…