JEE Maths - Ellipse

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Question - 1

Find the number of real tangents that can be drawn to the ellipse 3x2 + 5y2 = 32 passing through (3, 5)_____

  • A 2
  • B 4
  • C 12
  • D 24

Question - 2

A man running round a race course notes that the sum of the distances of two flag-posts from him is always 10 metres and the distance between the flag-posts is 8 meters. The area of the path he encloses is k\(\pi\) then find k______

  • A 5
  • B 10
  • C 15
  • D 20

Question - 3

An ellipse having foci at (3, 1) and (1, 1) passes through the point (1, 3). Then find its eccentricity_____

  • A 0.41
  • B 0.50
  • C 0.75
  • D 0.80

Question - 4

If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then fi,nd its latus rectum______

  • A 9.75
  • B 5.85
  • C 4.78
  • D 3.66

Question - 5

Suppose S and S'are foci of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\) If P is variable point on the ellipse and., if \(\triangle\) is area'of the triangle PSS', then find the maximum value of \(\triangle\)___

  • A 2
  • B 6
  • C 12
  • D 18

Question - 6

Tangent at a point P on \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) meets the x-axis at A and y-axis at B. The locus of the midpoint of AB is \(\frac{a^{2}}{x^{2}}+\frac{b^{2}}{y^{2}}=k\) then find k ________

  • A 4
  • B 12
  • C 16
  • D 24

Question - 7

Find the radius of the circle passing through the foci of ellipse \(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\) and having its centre (0, 3)____

  • A 4
  • B 12
  • C 16
  • D 20

Question - 8

S1, S2 are foci of an ellipse of major axis of length 10 units and P is any point on the ellipse such that perimeter of \(\triangle\)P S1 S2 is 15. Find the eccentricity of ellipse_____

  • A 0.50
  • B 0.25
  • C 1
  • D 1.5

Question - 9

If extuemities of diameter of the circle x2 + y2 = 16 are foci of an ellipse, then find the eccentricity of the ellipse, if its size is just sufficient to contain the circle____

  • A 0.70
  • B 0.50
  • C
  • D

Question - 10

If B and B' are the ends of minor axis and S and S' are the foci of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\)  then find the area of rhombus SBS'B' formed_____

  • A 12
  • B 24
  • C 32
  • D 64
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