Analytic Geometry Answers

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

7.Find the coordinate of the point of interception of the lines: 2x + y = 5 ; x + y = 3
a.(-1,2)
b.(1,2)
c.(1,-1)
d.(2,1)

8.The equation of a straight line at point (2,3) and slope 5 is given by
a.y=5x-3
b.y=5x-10
c.y=5x+3
d.y=3x-5

3.Find the coordinate of the point of interception of the lines: x + 2y = 5 ; x + y = 3
a.(1,2)
b.(−1,2)
c.(1,1)
d.(1,0)

4.Two lines are said to be parallel if
a.their gradient is the same
b.they have equal rate of change
c.the angle between the two lines is zero
d.All the options

1.Let the gradient of a line be 3, find the equation of the line at point(1,2)
a.2y=x
b.y=2x
c.y=x
d.y=3x

2.Find the equation of the line which is parallel to
3x−2y=5 and passes through the point (-2,-4)
a.3x+2y=−5
b.3x+2y=−2
c.(-3x+2y=-2)
d.(3x+2y=6)

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.