questionrEarly access

Ellipse

Showing 50 of 183 · 183 total
  1. 1.Let x^2f(a^2+7a+3)+y^2f(3a+15)=1 represent an ellipse with major axis along y-axis, where …
  2. 2.Let x=9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity is…
  3. 3.Let a focus of the ellipse E:x^2a^2+y^2b^2=1 be S(4,0) and its eccentricity be (4)/(5).
  4. 4.Let P(3 ,2 ), 0, be a point on the ellipse x^29+y^24=1,Q be a point on the circle x^2+y^2-…
  5. 5.Let an ellipse x^2a^2+y^2b^2=1
  6. 6.An ellipse has its center at (1, -2), one focus at (3, -2) and one vertex at (5, -2).
  7. 7.Let the length of the latus rectum of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a>b), be 30 .
  8. 8.Let each of the two ellipses E_1:x^2a^2+y^2b^2=1,(a>b) and E_2:x^2A^2+y^2B^2=1,(A<B) have …
  9. 9.If the points of intersection of the ellipses x^2+2 y^2-6 x-12 y+23=0 and 4 x^2+2 y^2-20 x…
  10. 10.Let the line y-x=1 intersect the ellipse (x^2)/(2)+(y^2)/(1)=1 at the points A and B .
  11. 11.Let S and S^' be the foci of the ellipse x^225+y^29=1 and P( , ) be a point on the ellipse…
  12. 12.If the line x+4y=√7, where R, touches the ellipse 3x^2+4y^2=1 at the point P in the first …
  13. 13.Let the ellipse 3x^2 + py^2 = 4 pass through the centre C of the circle x^2 + y^2 - 2x - 4…
  14. 14.Let the length of a latus rectum of an ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 be 10.
  15. 15.Let p be the number of all triangles that can be formed by joining the vertices of a regul…
  16. 16.Let for two distinct values of p the lines y=x+p touch the ellipse E:x^24^2+y^23^2=1 at th…
  17. 17.The centre of a circle C is at the centre of the ellipse E:x^2a^2+y^2b^2=1,a>b.
  18. 18.The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2,-3) and eccentr…
  19. 19.Let C be the circle of minimum area enclosing the ellipse E: (x^2)/(a^2)+(y^2)/(b^2)=1 wit…
  20. 20.A line passing through the point P(√5,√5) intersects the ellipse x^236+y^225=1 at A and B …
  21. 21.If the length of the minor axis of an ellipse is equal to one fourth of the distance betwe…
  22. 22.If S and S^' are the foci of the ellipse x^218+y^29=1 and P be a point on the ellipse, the…
  23. 23.If x+ y=109 is the equation of the chord of the ellipse x^29+y^24=1, whose mid point is ((…
  24. 24.Let the ellipse E_1: (x^2)/(a^2) + (y^2)/(b^2) = 1, a > b and E_2: (x^2)/(A^2) + (y^2)/(B^…
  25. 25.If the midpoint of a chord of the ellipse x^29+y^24=1 is (√2,4/3), and the length of the c…
  26. 26.The equation of the chord, of the ellipse (x^2)/(25)+(y^2)/(16)=1, whose mid-point is (3,1…
  27. 27.Let the product of the focal distances of the point (√3,(1)/(2)) on the ellipse x^2a^2+y^2…
  28. 28.The length of the chord of the ellipse (x^2)/(4)+(y^2)/(2)=1, whose mid-point is (1, (1)/(…
  29. 29.Let E:x^2a^2+y^2b^2=1,a>b and H:x^2A^2-y^2B^2=1.
  30. 30.Let f(x)=x^2+9,g(x)=(x)/(x-9) and a=f g(10),b=g f(3).
  31. 31.Let the line 2x+3y-k=0,k>0, intersect the x-axis and y-axis at the points A and B, respect…
  32. 32.Let P be a point on the ellipse x^29+y^24=1.
  33. 33.Let x^2a^2+y^2b^2=1,a>b be an ellipse, whose eccentricity is 1√2 and the length of the lat…
  34. 34.Let P be a parabola with vertex (2,3) and directrix 2 x+y=6.
  35. 35.Let A( ,0) and B(0, ) be the points on the line 5x+7y=50.
  36. 36.The length of the chord of the ellipse (x^2)/(25)+(y^2)/(16)=1, whose mid point is (1, (2)…
  37. 37.Let the tangent and normal at the point (3√3,1) on the ellipse x^236+y^24=1 meet the y-axi…
  38. 38.Let P(2√3√7,6√7),Q,R and S be four points on the ellipse 9x^2+4y^2=36.
  39. 39.If the radius of the largest circle with centre (2,0) inscribed in the ellipse x^2+4y^2=36…
  40. 40.Consider ellipses E_k:kx^2+k^2y^2=1,k=1,2, ,20.
  41. 41.Let a circle of radius 4 be concentric to the ellipse 15 x^2+19 y^2=285.
  42. 42.Let the ellipse E:x^2 + 9y^2 = 9 intersect the positive x and y-axes at the points A and B…
  43. 43.In a group of 100 persons 75 speak English and 40 speak Hindi.
  44. 44.If the normal at an end of a latus rectum of an ellipse passes through an extremity of the…
  45. 45.If tangents are drawn to the ellipse x2 + 2y2 = 2 at all points on the ellipse other than …
  46. 46.Consider the parabola P:y^2=4kx and the ellipse E:x^2a^2+y^2b^2=1.
  47. 47.Let A be the point (3, 0) and circles with variable diameter AB touch the circle x^2 + y^2…
  48. 48.Let (h,k) lie on the circle C:x^2+y^2=4 and the point (2h+1,3k+2) lie on an ellipse with e…
  49. 49.Let E_1:x^29+y^24=1 be an ellipse.
  50. 50.Let an ellipse with centre (1,0) and latus rectum of length (1)/(2) have its major axis al…