Q1 (a) Prove the Power of a point theorem: Two intersecting lines cut a circle at points A, B and C,D respectively. If the lines intersect at P, then |PA| · |PB| = |PC| · |PD|. (b) State and prove the converse of the Power of point theorem. (c) Use part (b) to show that the vertices of any rectangle are co-circular.

Q: of the tss plane passes threngh the point Cl,) and contains the line {x=t, Find the 9 =-2, 2= 2

A: According to the given information, it is required to find the equation of plane.

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: 1. Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them lie on a…

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Q: Show that three points P , Q, R are collinear (lie on a line)if and only if −→P Q × −→P R = 0.

A: Given: Show that three points P, Q, and R are collinear (lie on a line) if and only if PQ→×PR→=0

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: 4. Sketch the graph of both lines on the coordinate plane. Use the graph to solve the systen S2x +…

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Q: Find all points with coordinates of the form (a, a) that are a distance 3 from P(-2, 1).

A: Given: P(-2,1) and distance is 3. To find the other coordinate point.

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

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Q: 3. If a plane contains two distinct points Pi and P2 then show that it contains every point on the…

A: Solve the given

Q: # 7. If we invent the line at infinity in the projective plane, then it is possible to construct one…

A: Given that if we invent the line at infinity in the projective plane,then it is possible to…

Q: The graph of (x/a) + (y/b) + (z/c) = 1 is a plane for any non-zero numbers a, b, and c. Which planes…

A: The graph of given plane is,

Q: Find the ditection cosines of two lines which are connected by the regions 1-5m+3n=0 and…

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Q: If a plane contains two distinct points P1 and P2 then show that it contains every point on the line…

A: From Geometry: Line can be parallel to plane, intersect the plane or lie in the plane. Only third…

Q: 3. Verify Euler's formula for the plane graphs shown below. B (a) (b)

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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: The general solution of the DE xdy = ydx is a family of A lines passing through the origin B…

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Q: 5. Consider two distinct points [b1 in the and plane. Explain why the solutions of the equation det…

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Q: Three line segments AC, AB and BD shown in the figure have the lengths of 2, 3 and 5, respectively.…

A: Given: Three line segments AC, AB, and BD showed in the figure have the lengths of 2, 3, and 5,…

Q: In a certain​ city, the road system is set up like a Cartesian plane​ (x-y grid).   Point B is12…

A: Point A is  at origin (0,0) Point B is12 blocks east and 18 blocks north from point A. Point C is 18…

Q: Draw a plane perpendicular to the horizontal plane inclined to the vertical (vertical) plane at an…

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Q: The midpoint of a segment can be found using the formulas for a directed line segment, x = (X2-X1) +…

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Q: 1. Let A, B and C be the vertices of a right triangle in R with hypotenuse BC. Let D be the point on…

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Q: 5. Points P, Q, and R are collinear such that PQ: PR If a directed line segment begins at P(2,-4)…

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Q: Points F, G, and H are collinear such that FG: FH ==. If a directed line segment begins at F(-5,-1)…

A: Given,  A directed line segment begins at F-5, -1 and ends at H4, -1.  FGFH= 13  We have to find the…

Q: Find the point P' symmetric of the point P(-5, 13) with respect to the line 2x - 3y - 3 = 0

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

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Q: prove Theorem 4P.1 Theorem 4P.1 There are exactly six lines in the four-point geometry.

A: The known fact is that in four point geometry, any two distinct points have exactly one line on both…

Q: 3. Find the point (x1, x2) that lies on the line x + 5x2 = 7 and on the line x1 – 2x2 = -2. See the…

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Q: AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of…

A: Given in a circle of radius r, there are two chords AB and AC such that AB=2AC. Also, the distance…

Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

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Q: 1. Choose a point Q1 in between P and Q. Connect the two points P and Q1 to construct the secant…

A: Given: The graph of the function, y=fx.

Q: Through one of the two intersection points of two circles, a diameter in each of the circles is…

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Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

A: The given problem can be proved both by mathematically and by the definition. For your convenience I…

Q: 3. Consider the graph of z=r -y". (a) What shape are the traces parallel to the ry-plane? Are there…

A: given z=x2-y2 (A) what shape are the traces parallel to xy plane? are there any restricition on the…

Q: .) The locus of points equidistant from two given parallel lines in a plane is a. a line that is…

A: Locus is the set of all points that follow a certain path determined by one or more specified…

Q: In the diagram below, draw the two limiting parallel lines to the given line I and a point P on the…

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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: a) Find the equation of the plane th

A: The question is taken from the plane in which we have to find the equation of the plane and integral…

Q: 25. Prove analytically that the four diagonals joining opposite vertices of a rectangular…

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Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: x2+y2=4, z=0

Q: Consider the two points (4,2) and (10,4). The distance between them is:   The x co-ordinate of the…

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Q: 2. Find the exact distance between the point P(2, 7) and the line y = -2x + 1. Use of graphis…

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Q: The diagram shows AB graphed on a coordinate plane. B (4, 6) 6- -5 4 3 2 -5 -4 -3 -2 -1 4 -1- -2 3…

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Q: (a) If we mark off a distance t along the unit circle, starting at (1, 0) and moving in a…

A: Topic -  unit circle

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that, x2+z2=4y=0

Q: Prove that three points (x1, yl), (x2, y2) and (x3, y3) are collinear ( on the same straight line)…

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Q: Describe geometrically all points P(x, y, z) that satisfy the given condition. X = 1

A: Given the points P(x,y,z) that satisfy the condition x=1.