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Two Dimensional Analytical Geometry II - Two Marks Study Materials

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. Examine the position of the point (2,3) with respect to the circle x2+y2−6x−8y+12=0.

  2. Find the equation of the circle with centre (2,-1) and passing through the point (3,6) in standard form.

  3. 11x2−25y2−44x+50y−256 = 0

  4. Find centre and radius of the following circles.
     x2+y2+6x−4y+4=0

  5. Find centre and radius of the following circles.
    2x2+2y2−6x+4y+2=0

  6. Find the equation of tangent to the circle x2 +y2 + 2x - 3y - 8 = 0 at (2, 3).

  7. Find the length of the tangent from (2, -3) to the circle x2 + y2 - 8x - 9y + 12 = 0.

  8. Find the equation of the parabola with vertex at the origin, passing through (2, -3) and symmetric about x-axis

  9. If a parabolic reflector is 24 cm in diameter and 6 cm deep, find its locus.

  10. If the line y = 3x + 1, touches the parabola y2 = 4ax, find the length of the latus rectum?

  11. Find the locus of a point which divides so that the sum of its.distances from (-4, 0) and (4, 0) is 10 units.

  12. For the ellipse x2 + 3y2 = a2, find the length of major and minor axis.

  13. Find the eccentricity of the ellipse with foci on x-axis if its latus rectum be equal to one half of its major axis.

  14. Find the eccentricity of the hyperbola. with foci on the x-axis if the length of its conjugate axis is \({ \left( \frac { 3 }{ 4 } \right) }^{ th }\) of the length of its tranverse axis.

  15. Find the equation of the hyperbola whose vertices are (0, ±7) and e = \(\frac { 4 }{ 3 } \)

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