Analytic Geometry Answers

Find the transformation of the eqn 12x^2-2y^2+z^2=2xy if the origin is kept fixed and the axes are rotated in such a way that the direction ratio of the new axes are (1,-3,0);3,1,0;0,0,1

A container in the form of triangular prism as shown in figure below contains water at a 6 inches. Find the volume of water and the wet part of the conatiner

A positive triangle lake with a side length of 10m, each side should be planted with trees. Question: If the distance between the two trees is ≤ 5m, what's the MINIMUM number of trees needed?

Calculate the area of a triangle whose vertices are given by (3, −1, 2), (1, −1, 2) and (4, −2, 1)

A, B, C, D are the points i − k, − i + 2 j, 2i − 3k, 3i − 2 j − k respectively. Show that the
projection of AB on CD is equal to that of CD on AB . Also find the cosine of their inclination.

Find the vertices,eccentricity,foc and asymptotes of the hyperbola x^2/8-y^2/4=1.Also trace it.Under what condition on ⋋ the line x+⋋y=2 will be tangent to this hyperbola?explain geometrically

9.What is the parametric equation of a circle with centre (2,−1) and radius 3
a.y=âˆ′1−3sinθ
b.y=âˆ′1+3sinθ
c.None of the option
d.y=âˆ′1+3tanθ

10.The equation of a parabola with vertical axis is given by
a.y^2=4px
b.y=4px^2
c.x^2=4py^2
d.x^2=4py

3.Given that x + 2y + 3z =1, 3x + 2y + z = 4, x + 3y + 2z = 0. What is x,y and z?
a.7/4,−3/4,1/4
b.5/4,−2/4,¼
c.\(1,-3/4,1/4)
d.None of the option

4.What is the angle between the two linesâˆ′3x+4y=8 and âˆ′2xâˆ′8yâˆ′14=0?
a.14.63 degree
b.âˆ′14degree
c.−14.63degree
d.14 degree

1._____is defined as the locus of a point which moves so that it is always the same distance from the fixed point (called the focus) and a given line called the directrix
a.A parabola
b.A hyperbola
c.A helix
d.An eclipse

2.if a=a1i+a2j+a3k and b=b1i+b2j+b3k, then ab
a.a=a1+b1+2b1
b.abcosθ
c.absinθ
d.a1b1+a2b2+a3b3

9.What is the sum of −−→ −−→ −−→ −−→
AB,- CB,- CD,- ED


a.−−→
AC
b.−−→
AB
c.−−→
AE
d.−−→
BE

10.What is the gradient the line that passes through points A(-3,-2) and B(1,0)?
a.(1/3)
b.(1/2)
c.−1 ans
d.1