Conic Sections Test

Result

Conic Sections Test - 63

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Weekly Quiz Competition

Question 1
1 / -0

If the radius of the circle $$ x ^ { 2 } + y ^ { 2 } $$ - 18 x - 12 y + k = 0 be 11 then k =

A
347

B
4

C
-4

D
97

Solution
Question 2
1 / -0

The equations $$x=\frac{t}{4},y=\frac{t^2}{4}$$ represents

A
An ellipse

B
A parabola

C
A circle

D
A hyperbola

Solution
Question 3
1 / -0

The latus rectum of a parabola whose focal chord is PSQ such that SP=3 and SQ=2 is given by

A
24/5

B
12/5

C
6/5

D
23/5

Solution
Question 4
1 / -0

If $$\frac { (3x-4y-{ 1) }^{ 2 } }{ 100 } -\frac { (4x+3y-{ 1) }^{ 2 } }{ 225 } =1,$$ then
length latusrectum of hyperbola is-

A
$$\frac { 9 }{ 2 } $$

B
$$\frac { 40 }{ 3 } $$

C
9

D
$$\frac { 8 }{ 3 } $$
Question 5
1 / -0

If $$y ^ { 2 } - 2 x - 2 y + 5 = 0$$ is

A
a circle with centre $$( 1,1 )$$

B
a parabola with vertex

C
a parabola with directrix $$x = 3 / 2$$

D
a parabola with directrix
Question 6
1 / -0

The equation $$\dfrac{x^2}{10 - a} + \dfrac{y^2}{4 - a} = 1$$ , represents an ellipse , if

A
$$a < 4$$

B
$$a > 4$$

C
$$4 < a < 10$$

D
$$a > 10$$

Solution
Question 7
1 / -0

The equation of circle with centre (1, 2) and tangent $$x + y - 5 = 0$$ is

A
$${x^2} + {y^2} + 2x - 4y + 6 = 0$$

B
$${x^2} + {y^2} - 2x - 4y + 3 = 0$$

C
$${x^2} + {y^2} - 2x + 4y + 8 = 0$$

D
$${x^2} + {y^2} - 2x - 4y + 8 = 0$$

Solution
Question 8
1 / -0

The distance between the foci or a hyperbola is double the distance between its vertices and the length of a conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of coordinates is

A
$$

3 x ^ { 2 } - y ^ { 2 } = 3

$$

B
$$

x ^ { 2 } - 3 y ^ { 2 } = 3

$$

C
$$

3 x ^ { 2 } - y ^ { 2 } = 9

$$

D
$$

x ^ { 2 } - 3 y ^ { 2 } = 9

$$

Solution
Question 9
1 / -0

The equation of directrix of a parabola is 3x + 4y + 15 =0 and equation of tangent at vertex is 3x + 4y - 5= 0. Then the length of latus recturn is equal to

A
15

B
14

C
13

D
16

Solution
Question 10
1 / -0

Length of the latus rectum of the parabola $$25\left[ { \left( x-2 \right) }^{ 2 }+{ \left( y-3 \right) }^{ 2 } \right] ={ \left( 3x-4y+7 \right) }^{ 2 }$$ is

A
4

B
2

C
1/5

D
2/5

Solution