Parabola Test

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Parabola Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

If the line 2x – y + λ = 0 is a diameter of the circle x2+y2+6x−6y+5=0 then λ =

A
6

B
9

C
3

D
12

Solution

Equation of circle is x2+y2+6x−6y+5=0

x²+6x+y²−6y=−5

Applying completing the square method

(x+3)²+(y−3)²=(13√)²

Comparing the above equation with(x−h)²+(y−k)²=(r)² we get center as (-3,3) and radius as √ 13 .

As centre of the circlre lies on diameter , it will satisfy the equation of diameter, so on putting (-3,3) in equation of diameter we get

2(−3)−(3)+λ=0

=> −6−3−λ=0

=>λ=9
Question 2
1 / -0

Which of the following does not defines a parabola?

A
A plane curve formed by the intersection of a right circular cone with a plane parallel to a generator of the cone

B
The set of points in a plane that are equidistant from a fixed line and a fixed point in the same plane or in a parallel plane

C
It is the locus of a point sum of whose distances from two fixed points in a plane remains fixed

D
None of these
Question 3
1 / -0

The equation x²+y²=0 represents

A
an equilateral hyperbola.

B
pairs of straight line.

C
a degenerate circle.

D
an ellipse.

Solution

The above circle can be written as (x−0)2+(y−0)²=(0)²

Here the center is (0,0) and radius is also 0 units.

So it is a degenerate circle as degenerate circle is a circle( a point) where radius is zero units.
Question 4
1 / -0

A circle described on the focal radii of a parabola as diameter touches the

A
axis

B
tangent at the vertex

C
directrix

D
None of these
Question 5
1 / -0

The circles x²+y²+6x+6y=0 and x²+y²−12x−12y=0

A
cut orthogonally

B
ouch each other externally

C
intersect in two points

D
touch each other internally
Question 6
1 / -0

If e represents the eccentricity of a parabola, then

A
e = 1

B
0 < e < 1

C
e > 1

D
e = 0

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Re-Attempt Weekly Quiz Competition

Parabola Test - 1

Result

Parabola Test - 1

Score

-

Rank

-

SHARING IS CARING

Question 1

6

9

3

12

Solution

Question 2

A plane curve formed by the intersection of a right circular cone with a plane parallel to a generator of the cone

The set of points in a plane that are equidistant from a fixed line and a fixed point in the same plane or in a parallel plane

It is the locus of a point sum of whose distances from two fixed points in a plane remains fixed

None of these

Question 3

an equilateral hyperbola.

pairs of straight line.

a degenerate circle.

an ellipse.

Solution

Question 4

axis

tangent at the vertex

directrix

None of these

Question 5

cut orthogonally

ouch each other externally

intersect in two points

touch each other internally

Question 6

e = 1

0 < e < 1

e > 1

e = 0

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