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Prove that the curve represented by x=3(...

Prove that the curve represented by `x=3(cost+sint),y=4(cost-sint),t in R ,` is an ellipse

A

an elipse

B

a parabola

C

a hyperbola

D

a circle

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The correct Answer is:
A
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TARGET PUBLICATION-CIRCLE AND CONICS -CRITICAL THINKING
  1. Filnd the distance between the directrices the ellipse (x^2)/(36)+(...

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  2. The equation of the circle passing through the foci of the ellipse (x...

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  3. Prove that the curve represented by x=3(cost+sint),y=4(cost-sint),t in...

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  4. The length of the axes of the conic 9x^(2) + 4y^(2) - 4y + 1 = 0, are

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  5. The co-ordinates of the foci of the ellipse 3x ^(2) + 4y ^(2) -12 x -8...

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  6. The eccentricity of the ellipse 4x^2=9y^2=8x+36 y+4=0 is 5/6 b. 3/5 c....

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  7. An ellipse is described by using an endless string which is passed ove...

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  8. The length of the transverse axis of a hyperbola is 7 and it passes th...

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  9. If the centre, vertex and focus of a hyperbola be (0,0), (4,0) and (6,...

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  10. Equation of the hyperbola with eccentricity 3/2 and foci at (±2,0) is

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  11. If the latus rectum of an hyperbola be 8 and eccentricity be (3)/( sqr...

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  12. Find the equation of the hyperbola whose conjugate axis is 5 and th...

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  13. A hyperbola, centred at the prigin, has transverse axis 2a. If it pass...

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  14. The equation of the hyperbola whose foci are (6.5), (-4,5) and eccentr...

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  15. The equation of the hyperbola whose directrix is 2x+y=1, focus (1,1) a...

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  16. If e and e' be the eccentricities of two conics S=0 and S'=0 and if e^...

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  17. The vertices of the hyperbola 9x^(2)-16y^(2)-36x+96y-252=0 are

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  18. The equation of the directrices of the conic x ^(2)+ 2x - y ^(2) + 5=0...

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  19. The latus rectum of the hyperbola 9x ^(2) -16 y^(2) + 72x - 32y-16=0 i...

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  20. The locus of the point of intersection of the lines axsectheta+bytanth...

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