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### Maths MCQ Class XI Ch-11 | Conic Section

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## Mathematics MCQ Class XI Chapter-11

## Conic Section

*MCQ based on conic sections like circle Parabola, Ellipse, Hyperbola. Multiple Choice Questions on conic section chapter 11 class XI strictly according to the CBSE syllabus and pattern.*

## MCQ BASED ON CIRCLE CLASS XI

Question 1

Find the equation of circle with centre at origin and radius
5 units.

a) x^{2} + y^{2 }= 25

b) x^{2} + y^{2 }= 5

c) x^{2 }= 25

d) y^{2} = 25

Answer a

Question 2

The point (6, 2) lie ___________ the circle x^{2} + y^{2 }- 2x -4y – 36 = 0.

a) inside circle

b) outside circle

c) on the circle

d) either inside or outside

Answer c

Question 3

Find the equation of circle with centre at (2, 5) and radius
5 units.

a) x^{2} + y^{2 }+ 4x - 10y + 4 = 0

b) x^{2} + y^{2 }- 4x - 10y +
4 = 0

c) x^{2} + y^{2 } + 4x + 10y +
4 = 0

d) x^{2} + y^{2 } + 4x - 10y –
4 = 0

Answer b

Question 4

Find the centre of the circle with equation x^{2} + y^{2 }- 4x - 10y + 4 =
0.

a) (-2, 5)

b) (-2, -5)

c) (2, -5)

d) (2, 5)

Answer: d

Explanation: Comparing the equation with general
form x^{2} + y^{2 }+ 2gx + 2fy + c =
0, we get

2g = - 4 ⇒ g = - 2

2f = -10 ⇒ f = - 5

c = 4

Centre is at (-g, -f) i.e. (2, 5).

Question 5

Find the radius of the circle with equation x^{2} + y^{2 }- 4x - 10y + 4 =
0.

a) 25 units

b) 20 units

c) 5 units

d) 10 units

Answer: c

Question 6

The centre of
the circle 4x^{2} + 4y^{2} – 8x + 12y – 25 = 0 is

a) (-2, 3)

b) (1, -3/2)

c) (-4, 6)

d) (4, -6)

Answer: (b)
(1, -3/2)

Explanation:

Given circle
equation: 4x^{2} + 4y^{2} – 8x + 12y – 25 = 0

⇒ x^{2} + y^{2} –
(8x/4) + (12y/4) – (25/4) = 0

⇒ x^{2} +y^{2} -2x
+3y -(25/4) = 0 …(1)

As we know that the
general equation of a circle is x^{2 }+ y^{2 }+ 2gx + 2fy + c = 0,
and the centre of the circle = (-g, -f)

Hence, by comparing
equation (1) and the general equation,

2g = -2, ⇒ g = -1

2f = 3, ⇒ f = 3/2

Now, substitute the
values in the centre of the circle (-g, -f), we get,

Centre = (1, -3/2).

Question 7

If a circle pass through (2, 0) and (0, 4) and centre at
x-axis then find the radius of the circle.

a) 25 units

b) 20 units

c) 5 units

d) 10 units

Answer: c

Explanation: Equation of circle with centre at
x-axis (a, 0) and radius r units is

(x - a)^{2 }+ (y)^{2 }= r^{2}

⇒ (2 - a)^{2} + (0)^{2 }= r^{2}

And (0 - a)^{2 }+ (4)^{2 }= r^{2}

⇒ (a - 2)^{2 }= a^{2 }+ 4^{2} ⇒ (- 2)(2a
- 2) =16 ⇒ a – 1 = - 4 ⇒ a = - 3

So, r^{2} = (2 + 3)^{2 }= 5 ^{2 }⇒ r = 5 units.

Question 8

The center of the circle 4x² + 4y² – 8x + 12y –
25 = 0 is?

(a) (2,-3)

(b) (-2,3)

(c) (-4,6)

(d) (4,-6)

Answer a

Question 9

If a circle pass through (4, 0) and (0, 2) and centre at
y-axis then find the radius of the circle.

a) 25 units

b) 20 units

c) 5 units

d) 10 units

Answer: c

Question 10

The point (1, 4) lie ___________ the circle x^{2} + y^{2 }- 2x - 4y + 2 = 0.

a) inside circle

b) outside circle

c) on the circle

d) either inside or outside

Answer b

Question 11

The radius of the circle 4x² + 4y² – 8x + 12y –
25 = 0 is?

(a) √57/4

(b) √77/4

(c) √77/2

(d) √87/4

Answer c

## MCQ BASED ON PARABOLA CLASS XI

Question 1

Find the focus of parabola with equation y^{2} = 100x.

a) (0, 25)

b) (0, -25)

c) (25, 0)

d) (-25, 0)

Answer c

Question 2

Find the focus of parabola with equation y^{2} = - 100x.

a) (0, 25)

b) (0, -25)

c) (25, 0)

d) (-25, 0)

Answer d

Question 3

Find the focus of parabola with equation x^{2} = 100y.

a) (0, 25)

b) (0, -25)

c) (25, 0)

d) (-25, 0)

Answer a

Question 4

The focus of the
parabola y^{2} = 8x is

a) (0,
2)

b) (2,
0)

c) (0,
-2)

d) (-2,
0)

Answer: (b)
(2, 0)

Explanation:

Given parabola
equation y^{2} = 8x …(1)

Here, the
coefficient of x is positive and the standard form of parabola is y^{2} =
4ax …(2)

Comparing (1) and
(2), we get

4a = 8

a = 8/4 = 2

We know that the
focus of parabolic equation y^{2} = 4ax is (a, 0).

Therefore, the
focus of the parabola y^{2} =8x is (2, 0).

Question 5

The length of
the latus rectum of x^{2} = -9y is equal to

a) 3 units

b) - 3 units

c) 9/4 units

d) 9 units

Answer: (d) 9
units

Explanation:

Given parabola
equation: x^{2} = - 9y …(1)

Since the
coefficient of y is negative, the parabola opens downwards.

The general
equation of parabola is x^{2 }= - 4ay…(2)

Comparing (1) and
(2), we get

-4a = -9

a = 9/4

We know that the
length of latus rectum = 4a = 4(9/4) = 9.

Therefore, the
length of the latus rectum of x^{2} = -9y is equal to 9 units.

Question 6

The parametric
equation of the parabola y^{2} = 4ax is

a) x = at; y = 2at

b) x = at^{2};
y = 2at

c) x = at^{2};
y^{2 }= at^{3}

d) x = at^{2};
y = 4at

Answer: (b) x
= at^{2}; y = 2at

Question 7

Find the equation of latus rectum of parabola y^{2} = 100x.

a) x = 25

b) x = - 25

c) y = 25

d) y = - 25

Answer a

Question 8

Find the equation of latus rectum of parabola x^{2} = - 100y.

a) x = 25

b) x = - 25

c) y = - 25

d) y = 25

Answer c

Question 9

Find the equation of directrix of parabola y^{2}=-100x.

a) x = 25

b) x = - 25

c) y = - 25

d) y = 25

Answer a

Question 10

If a parabolic reflector is 20 cm in diameter
and 5 cm deep then the focus of parabolic reflector is

(a) (0 0)

(b) (0, 5)

(c) (5, 0)

(d) (5, 5)

Answer c

Question 11

The equation of parabola with vertex at origin the axis is
along x-axis and passing through the point (2, 3) is

(a) y² = 9x

(b) y² = 9x/2

(c) y² = 2x

(d) y² = 2x/9

Answer b

Question 12

Find the vertex of the parabola y^{2 }=
4ax.

a) (0, 4)

b) (0, 0)

c) (4, 0)

d) (0, -4)

Answer b

Question 13

Find the equation of axis of the parabola y^{2} = 24x.

a) x = 0

b) x = 6

c) y = 6

d) y = 0

Answer d

Question 14

Find the equation of axis of the parabola x^{2} = 24y.

a) x = 0

b) x = 6

c) y = 6

d) y = 0

Answer a

Question 15

Find the length of latus rectum of the parabola y^{2 }= 40x.

a) 4 units

b) 10 units

c) 40 units

d) 80 units

Answer c

Question 16

At what point of the parabola x² = 9y is the abscissa three times that of ordinate

(a) (1, 1)

(b) (3, 1)

(c) (-3, 1)

(d) (-3, -3)

Answer b

## MCQ BASED ON ELLIPSE CLASS - XI

Question 1

An ellipse has ___________ vertices and ____________ foci.

a) two, one

b) one, one

c) one, two

d) two, two

Answer d

Question 2

Find the coordinates of foci of ellipse (x/25)^{2 }+ (y/16)^{2 }= 1.

a) (±3, 0)

b) (±4, 0)

c) (0, ±3)

d) (0, ±4)

Answer a

Question 3

In an ellipse, the distance between its foci is
6 and its minor axis is 8 then its eccentricity is

(a) 4/5

(b) 1/√52

(c) 3/5

(d) 1/ 2

Answer c

Question 4

A rod of length 12 CM moves with its and always
touching the co-ordinate Axes. Then the equation of the locus of a point P on
the road which is 3 cm from the end in contact with the x-axis is

(a) x²/81 + y²/9 = 1

(b) x²/9 + y²/81 = 1

(c) x²/169 + y²/9 = 1

(d) x²/9 + y²/169 = 1

Answer a

Question 5

Find the coordinates of foci of ellipse (x/16)^{2 }+ (y/25)^{2 }= 1.

a) (±3, 0)

b) (±4, 0)

c) (0, ±3)

d) (0, ±4)

Answer c

Question 6

What is major axis length for ellipse (x/25)^{2 }+ (y/16)^{2 }= 1?

a) 5 units

b) 4 units

c) 8 units

d) 10 units

Answer d

Question 7

For the ellipse
3x^{2 }+ 4y^{2} = 12, the length of the latus rectum is:

b) 3/5

c) 3

d) 4

Answer: (c) 3

Explanation:

Given ellipse
equation: 3x^{2 }+ 4y^{2} = 12

The given equation
can be written as (x^{2}/4) + (y^{2}/3) = 1…(1)

Now, compare the
given equation with the standard ellipse equation: (x^{2}/a^{2})
+ (y^{2}/b^{2}) = 1, we get

a = 2 and b = √3

Therefore, a >
b.

If a>b, then the
length of latus rectum is 2b^{2}/a

Substituting the
values in the formula, we get

Length of latus
rectum = [2(√3)^{2}] /2 = 3

Question 8

What is minor axis length for ellipse (x/25)^{2 }+ (y/16)^{2 }= 1?

a) 5 units

b) 4 units

c) 8 units

d) 10 units

Answer c

Question 9

What is equation of latus rectums of ellipse (x/25)^{2 }+ (y/16)^{2 }= 1?

a) x = ±3

b) y = ±3

c) x = ±2

d) y = ±2

Answer a

Question 10

In an ellipse, the distance between its foci is 6 and the minor axis is 8, then its eccentricity is

a) 1/2

b) 1/5

c) 3/5

d) 4/5

Answer: (c)
3/5

Explanation:

Given that the
minor axis of ellipse is 8.(i. e) 2b = 8. So, b=4.

Also, the distance
between its foci is 6. (i. e) 2ae = 6

Therefore, ae = 6/2
= 3

We know that b^{2} =
a^{2}(1-e^{2})

b^{2} =
a^{2} – a^{2}e^{2}

b^{2} =
a^{2} – (ae)^{2}

Now, substitute the
values to find the value of a.

(4)^{2} =
a^{2} -(3)^{2}

16 = a^{2} –
9

a^{2} =
16+9 = 25.

So, a = 5.

The formula to
calculate the eccentricity of ellipse is e = √[1-(b^{2}/a^{2})]

e = √[1-(4^{2}/5^{2})]

e = √[(25-16)/25]

e = √(9/25) = 3/5.

Question 11

A man running a race course notes that the sum of the
distances from the two flag posts from him is always 10 meter and the distance
between the flag posts is 8 meter. The equation of posts traced by the man is

(a) x²/9 + y²/5 = 1

(b) x²/9 + y2 /25 = 1

(c) x²/5 + y²/9 = 1

(d) x²/25 + y²/9 = 1

Answer d

## MCQ BASED ON HYPERBOLA CLASS XI

Question 1

A hyperbola has ___________ vertices and ____________ foci.

a) two, one

b) one, one

c) one, two

d) two, two

Answer d

Question 2

Find the coordinates of foci of hyperbola ^{2}−(y/16)^{2}

a) (±5,0)

b) (±4,0)

c) (0,±5)

d) (0,±4)

Answer a

Question 3

The equation of a hyperbola with foci on the
x-axis is

(a) x²/a² + y²/b² = 1

(b) x²/a² – y²/b² = 1

(c) x² + y² = (a² + b²)

(d) x² – y² = (a² + b²)

Answer b

a. e =1

b. e > 1

c. e < 1

d. 0 < e < 1

Answer: (b) e > 1

Question 5

Find the coordinates of foci of hyperbola ^{2}−(/x9)^{2}

a) (±5,0)

b) (±4,0)

c) (0,±5)

d) (0,±4)

Answer c

Question 6

What is transverse axis length for hyperbola ^{2}−(y/16)^{2}

a) 5 units

b) 4 units

c) 8 units

d) 6 units

Answer d

Question 7

What is conjugate axis length for hyperbola ^{2}−(y/16)^{2}

a) 5 units

b) 4 units

c) 8 units

d) 10 units

Answer c

Question 8

What is equation of latus rectums of hyperbola ^{2}−(y/16)^{2}

a) x = ±5

b) y = ±5

c) x = ±2

d) y = ±2

Answer a

Question 9

The length of the transverse axis is the distance between the ____.

a) Two vertices

b) Two Foci

c) Vertex and the origin

d) Focus and the vertex

Answer: (a)
Two vertices

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