Conic Sections Test

Result

Conic Sections Test - 65

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Weekly Quiz Competition

Question 1
1 / -0

The length of the latus rectum of the parabola $$4 y ^ { 2 } + 2 x - 20 y + 17 = 0$$ is

A
$$3$$

B
$$6$$

C
$$1 / 2$$

D
None
Question 2
1 / -0

The distance from the foci of P(a,b) on the ellipse $$\frac{x^{2}}{9}+\frac{y^{2}}{25}=1$$ are

A
$$4\pm \frac{5}{4}b$$

B
$$5\pm \frac{4}{5}a$$

C
$$5\pm \frac{4}{5}b$$

D
none of these

Solution
Question 3
1 / -0

The length of the latus rectum of the parabola $${ y }^{ 2 }-4x+4y+8=0\quad is$$

A
8

B
6

C
4

D
2
Question 4
1 / -0

The equation of circles passing through (3,-6) touching both the axes is

A
$$x^{2}+y^{2}-6x+6y+9=0$$

B
$$x^{2}+y^{2}+6x-6y+9=0$$

C
$$x^{2}+y^{2}-30x-30y+225=0$$

D
$$x^{2}+y^{2}-30x+30y+225=0$$

Solution
Question 5
1 / -0

If $$a\neq b$$ the parametric equations $$x=a(cos \Theta +sin \Theta ),y=b(cos\Theta -sin\Theta )$$ represents

A
Hyperbola

B
A circle

C
An ellipse

D
A pair of straight lines

E
A parabola

Solution
Question 6
1 / -0

The eccentricity of the hyperbola $$x^{2}-3y^{2}+1=0$$ is

A
$$\frac{1}{2}$$

B
1

C
2

D
3

Solution
Question 7
1 / -0

A common tangent to the conics $${ x }^{ 2 }=6y$$ and $$2{ x }^{ 2 }-4{ y }^{ 2 }=9$$, is __________.

A
$$x+y=1$$

B
$$x-y=1$$

C
$$x+y=\dfrac { 9 }{ 2 }$$

D
$$x-y=\dfrac { 3 }{ 2 } $$

Solution
Question 8
1 / -0

If the centroid of an equilateral triangle is (1,1) and one of its vertices is (-1,2) then, equation of its circum circle is

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

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

C
$$x^{2}+y^{2}-4x-6y+9=0$$

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

Solution
Question 9
1 / -0

The eccentricity of an ellipse, with its centre at the origin, is$$\frac{1}{2}$$. If one of the directrices is x = 4, then the equation of the ellipse is

A
$$3x^2 + 4y^2$$ = 1

B
$$3x^2 + 4y^2$$ = 12

C
$$4x^2 + 3y^2$$ = 12

D
$$4x^2 + 3y^2$$ = 1

Solution
Question 10
1 / -0

Angle between the parabola $$y^{2} = 4b(x - 2a + b)$$ and $$x^{2} + 4a(y - 2b - a) = 0$$ at the common end of their latus rectum, is

A
$$\tan^{-1}(1)$$

B
$$\cot^{-1}1 + \cot^{-1}\dfrac {1}{2} + \cot^{-1} \dfrac {1}{3}$$

C
$$\tan^{-1} (\sqrt {3})$$

D
$$\tan^{-1} (2) +\tan^{-1} (3)$$

Solution