Conic Sections Test

Result

Conic Sections Test - 60

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Weekly Quiz Competition

Question 1
1 / -0

The length of the latus rectum of the parabola, $$y^2-6y+5x=0$$ is

A
$$1$$

B
$$3$$

C
$$5$$

D
$$7$$

Solution
Question 2
1 / -0

The equation $${ x }^{ 2 }+{ y }^{ 2 }+4x+6y+13=0\quad $$ represents

A
Circle

B
Pair of coincident straight lines

C
Pair of concurrent straight lines

D
Point

Solution
Question 3
1 / -0

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

A
$$4$$

B
$$2$$

C
$$1/5$$

D
$$2/5$$

Solution
Question 4
1 / -0

If $$ P S Q $$ is the focal chord of the parabola $$ y^{2}=8 x $$ such that $$ S P=6 $$ . Then the length of $$SQ$$ is

A
$$6$$

B
$$4$$

C
$$3$$

D
none of these

Solution
Question 5
1 / -0

The equation of circle at center $$(3,4)$$ and radius $$5$$.

A
$$x^2+y^2-6x-8y=0$$

B
$$x^2+y^2+3x+4y+5=0$$

C
$$x^2+y^2+6x+8y=0$$

D
None.

Solution

The center of equation $$(3,4)$$
The radius of circle is $$5$$
The equation of circle is
$$(x-3)^2+(y-4)^2=5^2\\x^2+y^2-6x+9-8y+16=25\\x^2+y^2-6x-8y=0$$
Question 6
1 / -0

The curve for which the normal at any point (x,y) and the line joining origin to that point form and isosceles triangle with the x-axis as base is

A
an ellipse

B
a rectangular hyperbola

C
a circle

D
circle.

Solution
Question 7
1 / -0

If C is the centre and A, B are two points on the conic $${ 4x }^{ 2 }+{ 9y }^{ 2 }-8x-36y+4=0$$ such that $$\angle ABC-\dfrac { \pi }{ 2 } ,$$ then $$\begin{matrix} 1 & \quad \quad +\quad \quad \quad \quad \quad 1 \\ { CA }^{ 2 } & \quad \quad \quad \quad { CB }^{ 2 } \end{matrix}=$$

A
$$\dfrac { 13 }{ 36 } $$

B
$$\dfrac { 36 }{ 13 } $$

C
$$\dfrac { 16 }{ 33 } $$

D
$$\dfrac { 33 }{ 16 } $$

Solution
Question 8
1 / -0

If two distinct chords of a parbola $${ y }^{ 2 }=4ax$$ passing through (a , 2a) are bisected on the line x + y =1, then the length of the latnsrectum can be

A
2

B
1

C
4

D
3
Question 9
1 / -0

If the parabola $${y^2} = 4\,\,ax$$ passes through the point $$\left( { - 3,2} \right),$$ then the length of its latus rectum is

A
2 / 3

B
4 / 3

C
1 / 3

D
4

Solution

Question 10

1 / -0

Match the column I with column II and mark the correct option from the codes given below.

	Column I		Column II
i ii iii iv v	$$xy+a^2-a(x+y)$$ $$2x^2-72xy+23y^2-4x-28y-48=0$$ $$6x^2-5xy-6y^2+14x+5y+4=0$$ $$14x^2-4xy+11y^2-44x-58y+71=0$$ $$4x^2-4xy+y^2-12x+6y+9=0$$	p q r s	Ellipse Hyperbola Parabola Pair of straight lines

(i)$$=$$s,(ii)$$=$$q,(iii)$$=$$s,(iv)$$=$$p,(v)$$=$$s

(i)$$=$$p,(ii)$$=$$r,(iii)$$=$$q,(iv)$$=$$r,(v)$$=$$s

(i)$$=$$q,(ii)$$=$$p,(iii)$$=$$r,(iv)$$=$$s,(v)$$=$$q

(i)$$=$$r,(ii)$$=$$s,(iii)$$=$$p,(iv)$$=$$q,(v)$$=$$r

Solution

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Re-Attempt Weekly Quiz Competition

Conic Sections Test - 60

Result

Conic Sections Test - 60

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SHARING IS CARING

Question 1

$$1$$

$$3$$

$$5$$

$$7$$

Solution

Question 2

Circle

Pair of coincident straight lines

Pair of concurrent straight lines

Point

Solution

Question 3

$$4$$

$$2$$

$$1/5$$

$$2/5$$

Solution

Question 4

$$6$$

$$4$$

$$3$$

none of these

Solution

Question 5

$$x^2+y^2-6x-8y=0$$

$$x^2+y^2+3x+4y+5=0$$

$$x^2+y^2+6x+8y=0$$

None.

Solution

Question 6

an ellipse

a rectangular hyperbola

a circle

circle.

Solution

Question 7

$$\dfrac { 13 }{ 36 } $$

$$\dfrac { 36 }{ 13 } $$

$$\dfrac { 16 }{ 33 } $$

$$\dfrac { 33 }{ 16 } $$

Solution

Question 8

2

1

4

3

Question 9

2 / 3

4 / 3

1 / 3

4

Solution

Question 10

(i)$$=$$s,(ii)$$=$$q,(iii)$$=$$s,(iv)$$=$$p,(v)$$=$$s

(i)$$=$$p,(ii)$$=$$r,(iii)$$=$$q,(iv)$$=$$r,(v)$$=$$s

(i)$$=$$q,(ii)$$=$$p,(iii)$$=$$r,(iv)$$=$$s,(v)$$=$$q

(i)$$=$$r,(ii)$$=$$s,(iii)$$=$$p,(iv)$$=$$q,(v)$$=$$r

Solution

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