Conic Sections Test

Result

Conic Sections Test - 64

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Weekly Quiz Competition

Question 1
1 / -0

equation of latus rectum of the parabola $${ y }^{ 2 }-16x-6y+1=0$$ is

A
x-7=0

B
x+7=0

C
2x-7=0

D
2x+7=0
Question 2
1 / -0

The latus rectum of a parabola whose directrix is x + y- 2 =0 and focus is (3, -4) is

A
$$-3\sqrt { 2 } $$

B
$$3\sqrt { 2 } $$

C
$$2\sqrt { 2 } $$

D
$$3\sqrt { 2 } $$

Solution
Question 3
1 / -0

The equation $$\dfrac { { x }^{ 2 } }{ 12-a } +\dfrac { { y }^{ 2 } }{ 4-a } =1$$ represent an ellipse, if:

A
$$a < 12$$

B
$$ a < 4$$

C
$$ a > 12$$

D
$$ a > 4$$

Solution
Question 4
1 / -0

The y-axis is the directrix of the ellipse with eccentricity e=1/2 and the corresponding focus is at (3, 0), equation to its auxilary circle is

A
$$x^2+y^2-8x+12=0$$

B
$$x^2+y^2-8x-12=0$$

C
$$x^2+y^2-8x+9=0$$

D
$$x^2+y^2=4$$

Solution
Question 5
1 / -0

If e,e' be the eccentricities of two conics S and S' and if $$e^2+e^{,2}=3$$, then bothe S and S'

A
Ellipses

B
Parabola

C
Hyperbola

D
None of these

Solution
Question 6
1 / -0

If the circle describe on the line joining the points (0, 1) and $$(\alpha ,\beta )$$ as diameter cuts the x-axis in points whose abscissae are roots of equation $$x^2-x+3=0$$ the $$(\alpha ,\beta )$$

A
(1, 3)

B
(1, 5)

C
(-5, 1)

D
(-5, -1)

Solution
Question 7
1 / -0

The equation of the ellipse with axes along the x-axis and the y-axis, which passes through the points P(4, 3) and Q (6, 2) is

A
$$\frac{x^2}{50}+\frac{y^2}{13}=1$$

B
$$\frac{x^2}{52}+\frac{y^2}{13}=1$$

C
$$\frac{x^2}{13}+\frac{y^2}{52}=1$$

D
$$\frac{x^2}{52}+\frac{y^2}{17}=1$$

Solution
Question 8
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
none of these

Solution
Question 9
1 / -0

The equation of a circle with origin as a centre and passing through equilateral whose median is of length 3a is

A
$${ x }^{ 2 }+{ y }^{ 2 }={ 9a }^{ 2 }$$

B
$${ x }^{ 2 }+{ y }^{ 2 }={ 16a }^{ 2 }$$

C
$${ x }^{ 2 }+{ y }^{ 2 }={ a }^{ 2 }$$

D
None of these

Solution
Question 10
1 / -0

If the parabola $${ y }^{ 2 }=4ax$$ passes through (2,6) then the equation of the latusrectum is

A
2x -9 = 0

B
4x + 9 = 0

C
2x + 9 = 0

D
4x - 9 = 0

Solution