The locus of points P(x, y) such that that PA + PB= 5 given coordinates A(3, 0) andB(-1, 0) is:an ellipse with centre at the origina hyperbola«АВa line segment“Dan ellipse with centre (1, 0)-Ea circle with centre at the origin

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Answered: The locus of points P(x, y) such that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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All the chords of the hyperbola 3x² – y² – 2x + 4y = 0, %3D subtending a right angle at the origin, pass through the fixed point (A) (–1, 2) (В) (1, —2) (С) (2, —1) (D) (-2, 1)
Prove that the chords of contact of perpendicular tangents to the ellipse x2/a2 + y2 / b2 =1 touch another fixed ellipse x2/a4 + y2 / b4 =1/(a2 + b2 )
Find a parametric description for the ellipse (x-1)^2+9y^2=9, oriented counter-clockwise and where exactly one full revolution of the ellipse is achieved from 0<=t<=2
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The plane x+y+2z=4 intersects the paraboloid z=x^2+y^2 in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin
The left panel of Figure 3 shows an elliptic hyperboloid of two sheets given by 4x² - y² - 2² = 1. The middle panel shows the plane 2x space curves. With the plane removed for clarity, the right panel just shows the space curves and the hyperboloid.The magenta and navy space curves will be referred to as C₁ and C₂ respectively. y + z = k intersecting the two sheets, resulting in two -10 -10 -10 10 10 10 10 10 Zo -10 -10 0 10 Figure 3 The parametrisation used to plot these space curves is 2t2-4t+5 -10 10 Zo 10 -10 10 0 10 x(t) y(t) 4(t - 2) = t z(t) = 3- 4t 2(t-2) a) Find the domain of t for C₁ and C2 (1) དྱེསྱེºེ (2) (3) b) Using equations (1), (2) and (3) as a guide, determine the general space curve parametrisation in terms of k for the case presented above. This doesn't need to involve the 3 equations subbed directly into the hyperboloid/plane equations, just i.e sub the plane equation into the hyperboloid equation, leaving a relationship involving x,y and k; or y,z and k. Also,…

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The locus of points P(x, y) such that that PA + PB = 5 given coordinates A(3, 0) a B(-1, 0) is:« А an ellipse with centre at the origin В a hyperbola« C a line segment“ D an ellipse with centre (1, 0)- E a circle with centre at the origin