Conic Sections Test

Result

Conic Sections Test - 61

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Weekly Quiz Competition

Question 1
1 / -0

The latus rectum of parabola $${ y }^{ 2 }=5x+4y+1$$ is

A
10

B
5

C
$$\dfrac { 5 }{ 4 } $$

D
$$\dfrac { 5 }{ 2 } $$

Solution
Question 2
1 / -0

A circle touch the line L and the circle $${ C }_{ 1 }$$ externally such that both the circles are on the same side of the line, then the locus of center of the circle is

A
ellipse

B
hyperbola

C
parabola

D
parts of straight line

Solution
Question 3
1 / -0

If $$x ^ { 2 } + y ^ { 2 } - 2 x + 2 a y + a + 3 = 0$$ represents a real circle with non-zero radius, then most appropriate is?

A
$$a \in ( - \infty , - 1 )$$

B
$$a \epsilon ( - 1,2 )$$

C
$$a \epsilon ( 2 , \infty )$$

D
$$a \epsilon ( - \infty , - 1 ) \cup ( 2 , \infty )$$

Solution
Question 4
1 / -0

Equation of the circle whose radius is 3 and centre is $$(-1,2)$$

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

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

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

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

Solution
Question 5
1 / -0

If the equation $$p{ x }^{ 2 }+(2-q)xy+3{ y }^{ 2 }-6qx+30y+6q=0$$ represents a circle, then the values of p and q are

A
3, 1

B
2, 2

C
3, 2

D
3, 4

Solution
Question 6
1 / -0

The length of the lotus rectum of the parabola $$9x^{2}-6x+36y+19=0$$

A
$$36$$

B
$$9$$

C
$$6$$

D
$$4$$

Solution
Question 7
1 / -0

Equation of the circle whose radius is $$a+b$$ and centre $$(a, -b)$$

A
$${ x }^{ 2 }+{ y }^{ 2 }-2ax+2by=2ab$$

B
$${ x }^{ 2 }+{ y }^{ 2 }-2ax+2by=-2ab$$

C
$${ x }^{ 2 }+{ y }^{ 2 }-2ax+2by=ab$$

D
$${ x }^{ 2 }+{ y }^{ 2 }-2ax+2by=-ab$$

Solution
Question 8
1 / -0

The foci of a hyperbola with the foci of the ellipse $$\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 12 } =1.$$ Find the equation of the hyperbola, if its eccentricity is 2.

A
$$\frac { { x }^{ 2 } }{ 4 } -\frac { { y }^{ 2 } }{ 12 } =1$$

B
$$\frac { { x }^{ 2 } }{ 4 } -\frac { { y }^{ 2 } }{ 12 } =2$$

C
$$\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 12 } =1$$

D
None of these

Solution
Question 9
1 / -0

If $$ x^{2}+y^{2}-2 x+2 a y+a+3=0 $$ represents a real circle with non-zero radius, then most appropriate is

A
$$

a \in(-\infty,-0)

$$

B
$$

a \in(-1,2)

$$

C
$$

a \in(2,\infty)

$$

D
$$

a \in(-\infty,-1) \cup(2 \infty)

$$

Solution
Question 10
1 / -0

Find the equation of a circle whose cemtre is $$\left( {2,1} \right)$$ and radius is 3

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

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

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

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

Solution