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The locus of a point which moves so that...

The locus of a point which moves so that its distance from a fixed point, called focus, bears a constant ratio, which is less than unity, to its distance from a fixed line, called the directrix, is called

A

a parabola

B

a hyperbola

C

an ellipse

D

a circle

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The correct Answer is:
C
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A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. Radius of the sphere, with (2, -3, 4) and (-5, 6, -7) as xtremities of a diameter, is

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. The centre of the sphere (x-4)(x+4)+(y-3)(y+3)+z^2=0 is

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The equation of the locus of a point which moves so that its distance from the point (ak, 0) is k times its distance from the point ((a)/(k),0) (k ne 1) is

Find the locus of a point whose sum of the distances from the origin and the line x = 2 is 4 units.

OMEGA PUBLICATION-CONIC SECTIONS -Multiple Choice Questions (MCQs)
  1. The equation of the parabola with focus at (0, 3) and the directrix y ...

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  2. If the parabola y^2 = 4ax passes through (3, 2), then the length of ...

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  3. The locus of a point which moves so that its distance from a fixed po...

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  4. The foci of the ellipse 9x^2 +4y^2 =36 are

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  5. If the latus rectum of an ellipse is one half of its minor-axis, then...

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  6. The eccentricity of the conic 9x^2 +25y^2 =225 is

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  7. The foci of the hyperbola 9x^2 – 16y^2 = 144 are

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  8. If P (x,y) , F1(3,0) and F2 (-3,0) and 16x^2 +25y^2 =400 , then PF1+PF...

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  9. If the major axis of an ellipse is thrice the minor axis, then its ecc...

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  10. The latus rectum of the hyperbola 16x^2 -9y^2=144 is

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  11. The area of a circle centred at (1,2) and passing through (4, 6) is

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  12. The equation of a circle with centre at (1,0) and circumference 10pi ...

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  13. The equation of the circle whose centre is (0, 0) and which passes thr...

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  14. The ends of diameter of a circle are (2, 3) ,(6,5). The centre of the ...

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  15. The centre and radius of the circle x^2+(y-1)^2=2 are

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  16. The eccentricity 'e' of a parabola is

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  17. The equation of the directrix of the parabola x^2=-4ay is

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  18. The length of the latus rectum of the hyperbola x^2/a^2-y^2/b^2=1 is

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  19. If e is the eccentricity of the ellipse x^2/a^2+y^2/b^2 = 1 (a lt b) ,...

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  20. The latus rectum of the ellipse 5x^2+9y^2 = 45 is

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