The base of a triangle passes through a fixed point (f,g) and its sides are bisected respectively at right angles by the lines y2-8xy-9x2. Find the locus of its vertex.

Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

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Q: A point on the a-axis that is equidistant from the points (9, – 6) |(- 8, 6) is and

A: the given points are .................first point .................second point now the third point…

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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: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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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 distance (in appropriate units) between the points P(2,−1)P(2,−1)and Q(3,4)Q(3,4)in the…

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Q: Show that (km) is the number of paths in a square grid from (0,0) to the point (m,n) on the diagonal…

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Q: Find the distance from (4, –2, 6) to each of the following. a. The xy-plane

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Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 are parrallel.

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Q: Find b and c so that y = – 5z² + bz + c has vertex (9, 1). c =

A: The given equation y=-5x2+bx+c has a vertex at (9, 1). The given equation is an equation of a…

Q: Find the point (xo, yo) on the line 4x + 9y = 12 that is closest to theong1n.

A: Given: 4x+9y=12 Let the distance between the point (x0, y0) and origin be D As it is given that the…

Q: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

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Q: Find b and c so that y 9x2 + bx + c has vertex (– 10, – 5). || - - b = C = ||

A: Given y=-9x2+bx+c and vertex(-10,-5) We have to find b ,c

Q: Given the points F(8,4) and G(-7,-6) what are the coordinates of the point that partitions the…

A: Given that points are F8,4 and G−7,−6. We have to find the coordinates of the point that partitions…

Q: The planes x - 2y + 32 - 3 =0 and 3x + y - z + 5 =0 are perpendicular. Select one: True False

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Q: For what minimum integer value of a, will the line ax+(a+1),y=18 (a> 0) have two intersection points…

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Q: Find the points on the coordinate plane 2,3) and Q(2.-2.-1)

A: Given query is to find point P and Q on coordinate plane.

Q: Prove that the point (1,11),(2,15), and (-3,-5) are collinear and find the equation of the straight…

A: Let the given points be A (1,11), B (2,15), and C (-3,-5). Evaluate the slope of the line AB as…

Q: , and mz = X+ 20 A (3x) 20 -2 =180 x+20)° What is the value of x? What is the image of the point…

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Q: Find the locus of the points P(x, y) such that PA = 2PB where A is the point with coordinates (0, 3)…

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Q: Find all planes in R3 whose intersection with the xz-plane is theline with equation 3x + 2z = 5.

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

Q: Use the result in Exercise 21 to find the equation of the line that contains (5, – 1) and is…

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Q: Find the area of the triangle that lies in the first quadrant (with its base on the x-axis) and that…

A: y=2x-4 and y=-4x+20 We need to find the area of the triangle that lies in the first quadrant (with…

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: If l,, l2, and l3 are nonconcurrent lines, prove that there exist three points. Exactly one each…

A: Three or more points are said Lto be collinear if they all lie on the same straight line If l1 , l2…

Q: Find the Cartesian equation of the locus of points satisfying PA + PB = 12, where A is the point…

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Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

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Q: The planes x - 2y + 4z - 3 = 0 and 2x - y - z + 3 = 0 are perpendicular. Select one: True False

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Q: Find the shortest distance between the point A(2, 5, –7) and the plane 3x – 5y + 6z = 9.

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

Q: Show that -ydx+xdy) = x₁y₂-₂₁ where C is the line segment joining (x,y) and (x₂,₂).

A: We have to prove ∫C-ydx+xdy=x1y2-x2y1 Where C is the line segment joining x1,y1 and x2,y2 Now…

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 equation of locus of a point P such that the distance of P from the origin is twice the…

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Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to…

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 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: Use the result in Exercise 21 to find the equation of the line that contains (4, 5) and is…

A: Given- 2x+3y=6 To find- The equation of the line which is passing through the point 4,5 and…

Q: Find the coordinates of the intersection point of the lines x_1 + 3x_2 = 3 and −2x_1 + 4x_2 = 1 in…

A: Solved below

Q: find the equation of a locus of a point P such that distance of P from the origin is twice the…

A: Let us consider that, an arbitrary point P is x,y. Vertices of origin and point A are 0,0 and 1,2…

Q: Prove analytically that the midpoint of the hypotenuse of a right triangle is equidistant from the…

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Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: Determine the midpoint that lies between the two given points. (3π, 3) and (6π, 9)

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Q: What is the y-coordinate of all points in the xz-plane?

A: Plane: The y-coordinate of all points in the xz plane , i.e. we need to put y=0.

Q: Find the angle between the planes (x+y+za1)and. (x-24+32-1). And find the Symmetricequations for the…

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Q: Find the midpoint M of the line segment joining the points A = (6, –3) and B = (-2, 5). %3D

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Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: Among all the points on the graph of z = 10 - x2 - y2 that lie above the plane x + 2y + 3z = 0, find…

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Q: Find b and c so that y 1x? + bx + c has vertex - (– 2, 0). С —

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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..