Conic Sections Test

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Conic Sections Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

A and B are two distinct points, Locus of a point P satisfying |PA| + | PB | = 2k, a constant is

A
an ellipse

B
a hyperbola

C
the line segment [AB]

D
nothing can be said as we will not get any specific equation as k is not specified .

Solution

Since the value of k is not specified, we cannot get a specific equation.
Question 2
1 / -0

locus of the point of intersection of the lines x = sec θ + tan θ and y = sec θ – tan θ is

A
an ellipse

B
a parabola

C
a straight line

D
none of these

Solution

After solving the equations we will get x+y = 2sec θ which represents a linear equation.
Question 3
1 / -0

The vertex of the parabola y² = 4 a(x − a) is

A
( 0, a)

B
( 0, 0)

C
( a, 0)

D
none of these

Solution

y² = 4 a(x − a)

Let Y=y and X = x-a

for standard parbola Y²=4aX the vertex is (0,0)

so put X=0 and Y=0.

i.e. put x-a = 0 and y=0

so vertex is (a,0)
Question 4
1 / -0

The two parabolas x² = 4y and y² = 4x meet in two distinct points. One of these is the origin and the other is

A
(2, 2)

B
( 4, 4)

C
( 1, 1)

D
none of these

Solution

substituting for x² in equation (2)

y² = 4y. This implies y = 4

similarly substituting for y² in equation(1)

x² = 4x. This implies x = 4

Hence the other point point of intersection is (4,4)
Question 5
1 / -0

The equation of the directrix of the parabola x² = − 4ay is

A
x + a = 0

B
y – a = 0

C
y + a = 0

D
x – a = 0

Solution

From the equation we infer that the parabola is open downward.

Hence the directrix passes through the point (0,a) and will be parallel to the X-axis.

Hence the equation of the directrix is y = a or y - a = 0
Question 6
1 / -0

The eccentricity ‘e’ of a parabola is

A
Equal to 1

B
Zero

C
More than 1

D
Less than 1

Solution

Eccentricity of a parabola is 1

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Re-Attempt Weekly Quiz Competition

Conic Sections Test - 5

Result

Conic Sections Test - 5

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SHARING IS CARING

Question 1

an ellipse

a hyperbola

the line segment [AB]

nothing can be said as we will not get any specific equation as k is not specified .

Solution

Question 2

an ellipse

a parabola

a straight line

none of these

Solution

Question 3

( 0, a)

( 0, 0)

( a, 0)

none of these

Solution

Question 4

(2, 2)

( 4, 4)

( 1, 1)

none of these

Solution

Question 5

x + a = 0

y – a = 0

y + a = 0

x – a = 0

Solution

Question 6

Equal to 1

Zero

More than 1

Less than 1

Solution

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Score

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Rank

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