Multiple Choice QuestionsTwo sides of a rhombus are along the lines, x−y+1=0 and 7x−y−5=0. If its diagonals intersect at (−1, −2), then which one of the following is a vertex of this rhombus?
(−3, −9)
(−3, −8)
(1/3, -8/3)
(1/3, -8/3)
The centres of those circles which touch the circle, x2+y2−8x−8y−4=0, externally and also touch the x-axis, lie on:
a circle
an ellipse which is not a circle
a hyperbola.
a hyperbola.
If one of the diameters of the circle, given by the equation, x2+y2−4x+6y−12=0, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is:
5√2
5√3
5
10
Let P be the point on the parabola, y2=8x which is at a minimum distance from the centre C of the circle, x2+(y+6)2=1. Then the equation of the circle, passing through C and having its centre at P is:
x2+y2−4x+8y+12=0
x2+y2−x+4y−12=0
x2+y2− 4 x +2y−24=0
x2+y2− 4 x +2y−24=0
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is:
4/3
4/√3
2/√3
√3
The distance of the point (1, −5, 9) from the plane x−y+z=5 measured along the line x=y=z is:
3√10
10√3
10/√3
20/3
B.
10√3
the equation of the line passing through the point (1,5-9 and parallel to x =y=z is
Thus, any point on this line is of the form
(λ +1, λ-5 ,λ+9)
Now, if P (λ +1, λ-5, λ+9) is the point of intersection of line and plane, then
(λ+1) - (λ-5) +λ+9 = 5
λ +15 = 5
λ = -10
therefore coordinates of point P are (-9, -15,-1)
Hence, required distance
=
If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
3a2−26a+55=0
3a2−32a+84=0
3a2−34a+91=0
3a2−34a+91=0
Switch
lies in the plane lx +my -z = 9, then l2 +m2 is equal to 
be three unit vectors such that 
then the angle between 
is
