Coordinate Geometry Test

Result

Coordinate Geometry Test - 49

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

If the mid-point of chord of the ellipse $$ \frac{x^{2}}{16}+\frac{y^{2}}{25}=1$$ is (0,3) and length of the chord is $$\frac{4k}{5}$$, then k is

A
2

B
4

C
8

D
10

Solution
Question 2
1 / -0

Area of a triangle whose vertices are $$ (a \cos \theta, b \sin \theta),(-a \sin \theta, b \cos \theta) $$ and$$ (-a \cos \theta,-b \sin \theta) $$ is $$ - $$

A
a b sin $$ \theta \cos \theta $$

B
$$ a \cos \theta \sin \theta $$

C
$$ \frac{1}{2} a b $$

D
$$ a b $$

Solution
Question 3
1 / -0

If the area of triangle formed by the points (2a , b) (a + b , 2b + a) and (2b , 2a) be $$\lambda$$ , then the area of the triangle whose vertices are (a + b , a b) , (3b a , b + 3a) and (3a b , 3b a) will be

A
$$\dfrac{3}{2}\lambda$$

B
$$3\lambda$$

C
$$4\lambda$$

D
none of these

Solution
Question 4
1 / -0

If the sides of a triangle are $$\dfrac{x}{y}+\dfrac{y}{z} ; \dfrac{y}{z}+\dfrac{z}{x} ; \dfrac{z}{x}+\dfrac{x}{y}$$ then the area of the triangle is

A
$$xyz$$

B
$$1$$

C
$$\sqrt{\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}}$$

D
$$\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}$$
Question 5
1 / -0

If $${ p }_{ 1 },{ p }_{ 2 },{ p }_{ 3 }$$ are the altitudes of a triangle from its vertices $$A,B,C$$ and $$\triangle $$, the area of the triangle $$ABC$$, then $$\frac { 1 }{ { p }_{ 1 } } +\frac { 1 }{ { p }_{ 2 } } +\frac { 1 }{ { p }_{ 3 } } $$ is equal to-

A
$$\frac { s }{ \triangle } $$

B
$$\frac { s-c }{ \triangle } $$

C
$$\frac { s-b }{ \triangle } $$

D
$$\frac { s-a }{ \triangle } $$
Question 6
1 / -0

The centre of a circle passing through the points $$(7,-5),(3,-7)$$ and $$(3,3)$$ is

A
$$(5,6)$$

B
$$(5,-1)$$

C
$$(3,2)$$

D
$$(3,-2)$$

Solution
Question 7
1 / -0

If $$ (\sqrt{2x}+\sqrt{3y}^{2} -36(\sqrt{3x}-\sqrt{2y})^{2}=0$$ and $$\sqrt{2x}-\sqrt{3y}+4\sqrt{5}=0$$ represents an Issosceles traiangle with base angle $$tan^{-1}6$$ then its area is

A
4

B
8/3

C
$$8\sqrt{6}$$

D
9
Question 8
1 / -0

The area of the triangle formed by the straight line $$x+y=3$$ and the bisectors of the pair of straight lines $${ x }^{ 2 }-{ y }^{ 2 }+2y=1$$ is

A
1

B
2

C
3

D
6

Solution
Question 9
1 / -0

The centre of a circle passing through the points (0,0),(1,0) and touching the circle x$$^2 + y^2$$ = 9 is ;

A
(3/2, 1/2)

B
(1/2, 3/2)

C
(1/2, 1/2)

D
($$\dfrac{1}{2} \pm \sqrt{2}$$)

Solution
Question 10
1 / -0

A triangle has two of its vertices at (0, 1) and (2, 2) in the cartesioan plane. Its third vertex lies on the x-axis. If the area of the triangle is 2 square units then the sum of the possible abscissae of the third vertex, is -

A
-4

B
0

C
5

D
6

Solution