Find the equation of the conic of major axis on the x-axis, the center at (0,0) passing through (2, -V2 and latus rectum of V3 (x- 2)2 (y+ v2)? = 1 12 3 12 = 1 3 (x- 2)2 (y+ v2) = 1 3 12 = 1 12

Q: Q3\Find the parametric and symmetric equations of the line through the points (3,2,0) and (- 5,0,…

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Q: Find the tangent line to the ellipse 0y-x-8 0,-1,-√7 y = 14 0y=-√14x-7 O None of these ○ y = √7x-8 1…

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Q: (a) Find the center and radius of the sphere defined by x² + y² +2²-8x + 2y + 8 = 0. (b) Find the…

A: A sphere is object that is 3-D analogue to a 2-D circle. If its center at the point (a, b, c) and…

Q: Find the point on the hyperbola x²-9y² 9 where the line 5x + 12y = 9 touches it.

A: Solving                  5x+12y=9  or            y=9-5x12   and   x2-9y2=9  We have…

Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

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Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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Q: Find a set of parametric equations for the graph of y = 4x² + 2 using the parameter t = x – 3 O x =…

A: Given parameter- t=x-3 Then,  x=t+3

Q: (x + 6)2, y2 = 1 26 13 x² + y? = 9

A: Given. (X+6)²/26 +y²/13 = 1 X² +y² =9 We can solve the conics by algebraic mathod.

Q: P(x, y) is any point on the ellipse 16x\power{2} + 25y\power{2} = 400 and F\index{1}=(3,0),…

A: We have 16x2 + 25y2=400         or      x225+  y216=1        or       a2=25 and  b2=16

Q: find parametric equations for an object that moves along the ellipse (x^(2))/(4)+(y^(2))/(9)=1 that…

A: The objective of the question is to find the parametric equations for an object moving along the…

Q: What is the equation of family of central conics with common foci and axis. Determine its orthogonal…

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Q: consider the ellipse with foci at A(-12,-5) and B(12,5) and known point at (-2.5,6). If the x'-axis…

A: To find the equation for the ellipse in the xy-plane after the proper rotation, follow these…

Q: Study and draw the conic section Q(x, y) = 13x² + 13y² — 10xy = 36. -

A: Conic sections (including degenerate ones) are the sets of points whose coordinates satisfy a…

Q: The locus of the foot of the perpendicular from the centre of the hyperbola xy = c² on a variable…

A: Given hyperbola equation is  xy = c2 The parametric form of this hyperbola is  x = c t  and   y =…

Q: Find parametric equations and a parameter interval for the motion of a particle that moves along the…

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Q: Find the point on the sphere x^2+ y^2+ z^2= 9 farthest from the point (-1,-1,1).

A: To find the point on the sphere  that is farthest from the point , we can use the property that the…

Q: Use, 0 = 60°, to write the rotated conic section given below, in the x'y'-plane. x² - y² = 9 Select…

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