Two Dimensional Analytical Geometry - Important Question Paper

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50

    Part A

    10 x 1 = 10
  1. Straight line joining the points (2, 3) and (-1, 4) passes through the point \((\alpha,\beta)\) if

    (a)

    \(\alpha+2=7\)

    (b)

    \(3\alpha+\beta=9\)

    (c)

    \(\alpha+3\beta=11\)

    (d)

    \(3\alpha+\beta=11\)

  2. The slope of the line which makes an angle 45 with the line 3x- y = -5 are

    (a)

    1,-1

    (b)

    \(\frac{1}{2},-2\)

    (c)

    \(1,\frac{1}{2}\)

    (d)

    \(2,-\frac{1}{2}\)

  3. Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2\(\sqrt{2}\) is

    (a)

    x+y+2=0

    (b)

    x+y-2=0

    (c)

    \(x+y-\sqrt{2}=0\)

    (d)

    \(x+y+\sqrt{2}=0\)

  4. The coordinates of the four vertices of a quadrilateral are (-2,4), (-1,2), (1,2) and (2,4) taken in order. The equation of the line passing through the vertex (-1,2) and dividing the quadrilateral in the equal areas is

    (a)

    x+1=0

    (b)

    x+y=1

    (c)

    x+y+3=0

    (d)

    x-y+3=0

  5. The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3,4) with coordinate axes are

    (a)

    5,-5

    (b)

    5,5

    (c)

    5,3

    (d)

    5,-4

  6. The locus of a moving point P(a cos3θ, a sin3θ) is

    (a)

    \({ x }^{ \frac { 2 }{ 3 } }+{ y }^{ \frac { 2 }{ 3 } }={ a }^{ \frac { 2 }{ 3 } }\)

    (b)

    x2+y2=a2

    (c)

    x + y = a

    (d)

    \({ x }^{ \frac { 3 }{ 2 } }+{ y }^{ \frac { 3 }{ 2 } }={ a }^{ \frac { 3 }{ 2 } }\)

  7. AB = 12 cm. AB slides with A on x-axis, B on y-axis respectively. Then the radius of the circle which is the locus of ΔAOB, where O is origin is:

    (a)

    36

    (b)

    4

    (c)

    16

    (d)

    9

  8. The equating straight line with y-intercept -2 and inclination with x-axis is 135° is:

    (a)

    x+y-2=0

    (b)

    y-x+2=0

    (c)

    y+x+2=0

    (d)

    none

  9. The length of the perpendicular from origin to line is \(\sqrt{3}x-y+24=0\) is:

    (a)

    2\(\sqrt{3}\)

    (b)

    8

    (c)

    24

    (d)

    12

  10. If(1, 3) (2,1) (9, 4) are collinear then a is:

    (a)

    \(\frac{1}{2}\)

    (b)

    2

    (c)

    0

    (d)

    -\(\frac{1}{2}\)

  11. Part B

    6 x 2 = 12
  12. If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x=a cos3, y=a sin3 θ.

  13. Find the value of k and b, if the points P(-3,1) and Q(2,b) lie on the locus of x2 - 5x + ky= 0.

  14. Find the equation of the locus of a point such that the sum of the squares of the distance from the points (3,5), (1,-1) is equal to 20.

  15. If O is origin and R is a variable point on y2 = 4x, then find the equation of the locus of the mid-point of the line segment OR.

  16. The coordinates of a moving point P are \((\frac{a}{2}(cosec\theta+sin\theta),\frac{b}{2}(cosec\theta-sin\theta))\) , where θ is a variable parameter. Show that the equation of the locus P is b2x2-a2y2=a2b2

  17. The sum of the squares of the distances of a moving point from two fixed points (a, 0) and (-0, 0) is equal to 2c2. Find the equation to its locus.

  18. Part C

    6 x 3 = 18
  19. Find the equation of the lines passing through the point (1,1) 
    (i) with y-intercept (-4)
    (ii) with slope 3
    (iii) and (-2, 3)
    (iv) and the perpendicular from the origin makes an angle 60° with x- axis.

  20. If p (r, c) is mid - point of a line segment between the axes, then show that \(\frac{x}{r}+\frac{y}{c}=2\)

  21. If P is length of perpendicular from origin to the line whose intercepts on the axes are a and b , then show that \(\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}\)

  22. The normal boiling point of water is 100°C or 212°F· and the freezing point of water is 0 °C or 32°F.
    (i) Find the linear relationship between C and F.
    (ii) Find the value of C for 98.6°F and 
    (iii) Find the value of F for 38°C.

  23. Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1.

  24. Show that the points (1, 3), (2, 1) and \((\frac{1}{2},4)\) are collinear, by using
    (i) concept of slope
    (ii) a straight line
    (iii) any other method.

  25. Part D

    2 x 5 = 10
  26. Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y - 15 = 0 are paralle llines.

  27. If (-4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x - y + 7 = 0, then find the equation of another diagonal.

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