Which of the following is NOT a formula for finding the distance between two points on the coordinate plane? O d = v( [(x_2-x_1)) ^2 - ((y_2-y_1)) ^2) O d = v( [(x_2-x_1)) ^2 + ( Ky_2-y_1)) ^2) O d = |y2 - y1|| O d = | x2 – x1||

Q: *5. Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that…

A: To prove that no two lines in hyperbolic geometry are equidistant from one another , first we…

Q: Calculate the distance between the points J (-7,0) and L= (-2,-4) in the coordinate plane. Give an…

A: Given,            Two points J(-7,0) and L(-2,-4) in coordinate plane we need to calculate distance…

Q: A line is tangent to the curve y = 3x1 and is bounded by the r- and y-axis in the first quadrant.…

A: Let's find.

Q: 29-31 Explain, in terms of linear approximations or differen- tials, why the approximation is…

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Q: Find the distance from the origin to the plane 2 = z - x.

A: Given point is (0,0,0) Given plane is 2=z-x or x-z+2=0

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

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

A: Answer

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: What is the maximum vertical distance between the line y = x + 51 and the parabola y= x² over the…

A: Given: The line y=x+51 and the parabola y=x2 To find: Maximum vertical distance between given line…

Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

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Q: 8. At what point of the parabola is the tangent line parallel to 7x+y-2=0? y = 2r-3x +1 O (1,0) O…

A: Here is the solution:

Q: Find the point Q that is on the curve nearest %3D the point (4, 1)

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Q: Find the point(s) on x = 3 - y that are closest to point A = (1,0).

A: Given: Curve x=3-y2 and a point A(1,0).

Q: Find the midpoint of these two points (4, 6) and (7, 10) Use the formulas: x = (x1 + x2)/2 %3D y (yi…

A: Consider the points, 4,6      and         7,10 The midpoints of two points is given by the formula,…

Q: Calculate the distance between the points P = (-7, 2) and M= (1, –1) in the coordinate plane. Give…

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Q: The coordinates of a point in the xy-coordinate system are given. Assuming that the XY-axes are…

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Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: The distance between the points (x,y) and (2,3) is 1) |x-2|+|y-3| 2) Sqrt(x-2)2+(y-3)2 3)…

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Q: where should the point P be chosen on the line segment AB so as to maximize the angle theta

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: Find the points on the graph of z = xy +8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

A:

Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: and the line perpendicular to Find the area of a triangle bounded by the y axis, the tine f(z) - 9 -…

A: We have to find the area of the region bounded by the y-axis, the line f(x)=9-67x, and the line…

Q: Show that the locus of the point whose distance from Y-axis is thrice its distance from (1,2,-1 ) is…

A: First of all we will suppose an arbitrary point and then try to find its locus using the given…

Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

A:

Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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Q: 3. Use the distance formula to prove that the point (4,2) is on the parabola x = Sy. Prenared hu

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Q: Iz+ai| rupriants Prove that the equation Iz+2] = 5V13 the origin is distance from pror line and its

A: Prove that the equation z+2=z+3i represents a line and its distance from the origin is 51326.

Q: A point moves such that the ratio of its distances from two fixed point is constant, show that its…

A: Let the moving point be P (x, y, z). Let A(a, 0, 0) and B(-a, 0, 0) be two fixed points.

Q: Calculate the distance between the points K=(-3, -2) and c=(1, 1) in the coordinate plane. Give an…

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

A: Given,             Point  (3, 1, −2)          Plane   x + 2y − 2z = 4

Q: Calculate the distance between the points P = (-7, 6) and N=(-2, 2) in the coordinate plane. Give an…

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Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Calculate the distance between the points M=(-9,8) and L=(-1, 1) in the coordinate plane. Give an…

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Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

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Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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Q: 1. Find the distance from the point to the given line by using the distance theorem…

A: Suppose the line l is Ax+By+C=0 and any point is P0x0, y0. Then the distance from the point P0 to…

Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

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Q: Find all yy such that the distance between the points (3, -8) and (-10, yy) is 19

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Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: By means of Lagrange's formula, prove that 1 Yo = - 1 - [2 (y₁+y_₁). (Y3 - y₁) 2 -Y₁) - 2 (Y-₁-y-3)…

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Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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Q: find the location of a point xyz that satisfies the condition I) xy<0, z=3 ii) |x|<2

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Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

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Q: What is the maximum vertical distance between the line y = x + 29 and the parabola y = x² over the…

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Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

Q: Find the points on the graph of z = xy + 8y-1 where the tangent plane is parallel to 6x + 5y + 6z =…

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Q: Three runners start at the same location and, at the same time, start running in different…

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