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Find the eccentricity of an ellipse (x^(...

Find the eccentricity of an ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` whose latus reactum is half of its major axis.

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Find the eccentricity of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 whose latus rectum is half of its major axis.

the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))=1 whose latus rectum is half of its minor axes , is

If the eccentricity of the ellipse, x^2/(a^2+1)+y^2/(a^2+2)=1 is 1/sqrt6 then latus rectum of ellipse is

Find the eccentricity of the ellipse (i) whose latus rectum is equal to half of its minor axis (ii) whose latus rectum is equal to half of its major axis (iii) if the major axis is three times the minor axis

If the length of the major axis intercepted between the tangent and normal at a point P (a cos theta, b sin theta) on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 is equal to the length of semi-major axis, then eccentricity of the ellipse is

Find the eccentricity of the ellipse whose latus rectum is (i) half its major axis, (ii) half its minor axis.

If eccentricity of the ellipse (x^(2))/(a^(2)+1)+(y^(2))/(a^(2)+2)=1 is (1)/(sqrt6) , then the ratio of the length of the latus rectum to the length of the major axis is

Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the positive end of the latus rectum.

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the minor axis, then prove that eccentricity is constant.

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the monor axis, then prove that eccentricity is constant.

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), ...

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  2. A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the ...

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  3. Find the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 ...

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  4. The slopes of the common tangents of the ellipse (x^2)/4+(y^2)/1=1 and...

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  5. Find the locus of the midpoints of chords of hyperbola 3x^(2)-2y^(2)+4...

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  6. The coordinates of the vertices Ba n dC of a triangle A B C are (2,...

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  7. If the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 make angles a...

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

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  9. Find the condition on a and b for which two distinct chords of the hyp...

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  10. The point of intersection of the tangents at the point P on the ellip...

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  11. Find the equation of the ellipse (referred to its axes as the axes o...

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  12. Tangents are drawn to the ellipse x^2/a^2+y^2/b^2=1 at two points who...

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  13. The sum of the squares of the perpendiculars on any tangents to the ...

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  14. A rod of length 12 cm moves with its ends always touching the coord...

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  15. Tangents are drawn from the points on the line x−y−5=0 to x^2+4y^2=4, ...

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  16. If alpha-beta= constant, then the locus of the point of intersection o...

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  17. Two circles are given such that one is completely lying inside the ...

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  18. How many real tangents can be drawn from the point (4, 3) to the hy...

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  19. For an ellipse x^2/9+y^2/4=1 with vertices A and A', drawn at the poin...

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  20. The first artificial satellite to orbit the earth was Sputnik I. It...

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