# 7. If we invent the line at infinity in the projective plane, then it is possible to construct one line perpendicular to a given line at a given point. Assuming this is true, given triangle ABC, which of the following is still impossible to construct using only projective geometry? (A) the orthocenter (C) the circumcenter (B) the incenter (D) the centroid

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: What is the equation of the line that is paralel to y-3r+ 12. passing through (4, 2), witten in…

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Q: Let the curve C be the mirror image of the parabola y" the line x+y + 4 = 0 If A and B are the…

A: Given: Parabola:y2=4xLine:x+y+4=0   A and B are the points of intersection of C with the line y=−5…

Q: nd the equation of the tangent to the circle X^2+Y^2-8X+2Y+7=0 at point (3,2), given that point…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The graph shows the normal lines from the point (2, 0) to the graph of the parabola x = y2 . How…

A: Given  Equation of parabola is x = y2 . To find slope of the normal line. first find the slope of…

Q: 1. Using Euler's equation, show that the shortest distance between two points (r1, yn, z1) and (r2,…

A: Given, the points are (x1, y1, z1)   and  (x2, y2, z2).

Q: What is the length of the latus rectum of the curve x2=-12

A: Answer

Q: Plot the points (with whole number coordinates) that satisfy the equation below and fit onto the…

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Q: 1. Given to the right is the graph of a portion of four curves: x = 0, y = 1, x – V3y = 0 and a? +…

A: Given: slope of line,m values.... Let us solve step by step

Q: What is the equations of the tangent line in the given plane 1. Tangent to the parabola z = x^2 +…

A: The given surface is:…

Q: 6. Determine the equation of the circle whose center is at (4, 5) and tangent to the circle whose…

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

Q: The graph shows the normal lines from the point (2,0) to the graph of the parabola x = y?. How many…

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Q: 4 Find a. the equations of the tangents to the circle x'+y +4x-2y-24 0 at the points where the…

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Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

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Q: The curve y et and the lines y = 0, x = 0, and x = In 2 %3D

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Q: 1. Let P(1, yı) be a point on the parabola r = 4py, p> 0, with focus F(0, p). Let a be the angle…

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Q: Question #8 I need the curves as well

A: Question #8 The provided sample means are shown below: Xˉ1=12.3\bar X_1 = 12.3 (For those taking the…

Q: 4 Find a. the equations of the tangents to the circle x + y +4x - 2y - 24 = 0 at the points where…

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Q: Suppose we follow Sir Isaac Barrow's method of finding the tangent implicitly for the circle with…

A: given equation of circle  x2+y2=9 using Sir Isaac Barrow's method and replace x,y→x-e, y-a equation…

Q: Consider the line which passes through the point P(3, -1, -1), and which is parallel to the line x =…

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Q: Find the DE of the family of plane curves described and sketch some of its members. Straight lines…

A: In the figure the blue straight lines are members of some of family which are tangents to the given…

Q: A circle has a center at the origin and has a radius of R. If x = 10 and y = 20, determine the slope…

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Q: Problem 4: For what valnes of a and o s the line y=-2x+b tangent to the parabola y=Ox° whern X=2?

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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: 7. Given that the line y = r -b is an asymptote to the ar curve y a,b €R,rz 1, then b = A -1-a 1-a C…

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Q: . Suppose that A = 2, 5 are the coordinates of a point inthe xy-plane (a) Find the coordinates of…

A: Consider a coordinate x,y. Then, if the coordinate is shifted a units towards left, the new…

Q: 1. XY is the same as YX. 2. XY is the same as YX. 3. HAB and AC are opposite rays, then they are…

A: As per our guideline we are allowed to do 1 question or 3 subparts at a time. Please post other…

Q: Here are the graphs of the circle centered at (0,0) with radius 8 and the line given by 4x +7y = 65.…

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Q: Find the length of the following three-dimensional curve r(t) = (1+ 3t,4 - 3t, – 6 + 2t) , for 1sts7

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Q: O1- The straight-line AB of true length 12 cms, is inclined 20 ° to H.P., and having the following…

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Q: 1 5. Trace the curve r = 2 - sinocos³o.

A: Since, you have post multiple question. I am answering the first one. Please post the question with…

Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

A: We will solve the problem

Q: 4.) The locus of points at a given distance from a given line in space is a. A cylindrical surface…

A: In a cylinder, if we consider the axis of the cylinder as a line, all the points on the surface of…

Q: Find the length of the following three-dimensional curve. r(t) = (2+5t,9-3t, -6+3t), for 1st≤4

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Q: In Pi Jinxing's dream, two curves are said to be CoRoNaViRaL if whenever they intersect, the two…

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Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Verify that the two families of curves are orthogonal, where C and K are real numbers. Use a…

A: xy=C,  x2-y2=K Consider, xy=C Differentiating with respect to x, we get…

Q: Let C be the curve starting at -3,3) and going along a straight line to 3,-3) and then…

A: We will use basic knowledge of line integral and curve parametrization to solve this question

Q: is cut by the plane given by y = the point (1, 3, -8). 3x, producing a curve in the plane. Find the…

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Q: 1. Let P(x1, Y1) be a point on the parabola x?: be the angle between the parabola and the line…

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Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

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Q: O1- The straight-line AB of true length 12 cms, is inclined 25 ° to V.P., and having the following…

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Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: 4 Find a. the equations of the tangents to the circle x +y +4x-2y – 24 = 0 at the points where the…

A: Given,  (a) Equation of the circle   x2+y2+4x-2y-24 = 0  We have to find the equations of tangents…

Q: Graph the line that is described parametrically by (x, y) (2t, 5- t), the... %3D (a) Confirm that…

A: As per our guidelines we are supposed to answer only one question at a time. So submit other…

Q: Find the DE of the family of plane curves describe and sketch some of its members. Straight lines…

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Q: Evaluate S,(x – 3y² + z) ds for each of the following curves. |

A: We have to find the line integral.

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.