Parabola Test

Result

Parabola Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

What does the curve C1 represent?

A
Circle

B
Ellipse

C
Parabola

D
Hyperbola
Question 2
1 / -0

What does the curve C2 represent?

A
Circle

B
Ellipse

C
Parabola

D
Hyperbola
Question 3
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 4
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 5
1 / -0

What does the curve C represent in the adjoining figure?

A
Circle

B
Ellipse

C
Disk

D
None of these
Question 6
1 / -0

What does the curve C represent in the adjoining figure?

A
Circle

B
Parabola

C
Two parabolas

D
None of these
Question 7
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 8
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 9
1 / -0

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

A
cut orthogonally

B
touch each other externally

C
intersect in two points

D
touch each other internally

Solution

Given equation of circles are,

x² + y² + 6x + 6y = 0 ...(i)

x² + y² - 12x - 12y = 0 ...(ii)

Here, g₁ = 3, f₁ = 3, g₂ = - 6 and f₂ = - 6

∴ Centres of circles are C₁(- 3,- 3) and C₂(6, 6) respectively and radii are r₁ = 3√2 and r₂ = 6√2 respectively.
Question 10
1 / -0

If e represents the eccentricity of a parabola, then

A
e = 1

B
0 < e < 1

C
e > 1

D
e = 0
Question 11
1 / -0

Which of the curves represented in the adjoining diagram represent(s) a parabola?

A
C4

B
C3

C
Both C3 and C4

D
None of these
Question 12
1 / -0

If the normal chord at a point 't' on the parabola y² = 4ax subtends a right angle at the vertex, then t² =

A
4

B
2

C
1

D
3
Question 13
1 / -0

The slopes of tangents drawn from a point (4, 10) to the parabola y² = 9x are

A
,

B
,

C
,

D
None of these
Question 14
1 / -0

The straight line x + y = k touches the parabola y = x – x² if k equals

A
0

B
– 1

C
1

D
None of these
Question 15
1 / -0

Length of common chord of the circles
x²+y²+2x+6y=0 and
x²+y²−4x−2y−6=0 is

A
√106

B
2√106

C
2/5√106

D
1/5√106

Solution
Question 16
1 / -0

Which of the following is an equation of a parabola?

A
y² = 6x² + 3x

B
y² = 6x⁴ + 3

C
y² = 6x² + 3

D
y² = 4x +4y
Question 17
1 / -0

The graph of which of the following polynomials will result in a parabola?

A
Cubic polynomial

B
Quadratic polynomial

C
Biquadratic polynomial

D
Linear polynomial
Question 18
1 / -0

The coordinates of an endpoint of the latus rectum of the parabola (y – 1)² = 4(x + 1) are

A
(0, – 3)

B
(0, – 1)

C
(0, 1)

D
(1, 3)
Question 19
1 / -0

Which of the following lie)s) on a parabola?

A
Focus of the parabola

B
Vertex of the parabola

C
Centre of the parabola

D
All of the above
Question 20
1 / -0

The equation(x²+y²)+5x−7y−2=0 represents

A
a circle

B
a pair of straight lines

C
an empty set

D
a degenerate circle

Solution

Explanation:
The general equation of the circle is x²+y²-2gh-2fy+c = 0. Sice the given equations satisfies the general equation, it represents the equation of the circle.