Circles Test

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Circles Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

x = a cos t, y = a sin t is the parametric form of a/an

A
circle

B
parabola

C
ellipse

D
hyperbola
Question 2
1 / -0

A circle passes through the origin and cuts intercepts a and b on the axes. The equation of the circle is

A
x² + y² – ax – by = 0

B
x² + y² + ax + by = 0

C
x² + y² – ax + by = 0

D
x² + y² + ax – by = 0
Question 3
1 / -0

The area of a circle with centre (h, k) and radius a is

A
π (h² + k² – a²)

B
π a²hk

C
π a²

D
None of these
Question 4
1 / -0

If the centre of a circle is (2, 3) and a tangent to the circle is x + y = 1, then the equation of this circle is

A
(x – 2)² + (y – 3)² = 8

B
(x – 2)² + (y – 3)² = 3

C
(x + 2)² + (y – 3)² = 2√2

D
(x – 2)² + (y – 3)² = 2√2
Question 5
1 / -0

Find the center and the radius of the circle (x + 5)² + (y + 7)² = 36.

A
(– 5, – 7) and 6

B
(– 6, – 9) and 36

C
(15, 4) and 6

D
(19, 5) and 6
Question 6
1 / -0

The equation of a circle with centre (4, 3) and touching the circle x² + y² = 1, is

A
x² + y² + 8x – 6y + 9 = 0

B
x² + y² + 8x + 6y – 11 = 0

C
x² + y² + 8x – 6y – 9 = 0

D
none of these
Question 7
1 / -0

A circle is inscribed in an equilateral triangle of side a. The area of any square inscribed in the circle is

A
a²/3

B
2a²/3

C
a²/6

D
a²/12
Question 8
1 / -0

Let C be any circle with centre (0, √2). How many rational points are there on C?

A
At most one

B
At most two

C
Infinite

D
None of these
Question 9
1 / -0

The number of tangents to the circle x²+y²−8x−6y+9=0, which pass through the point ( 3, - 2), is

A
1

B
2

C
0

D
none of these

Solution

x2+y2−8x−6y+9=0

After completing the square,we get

(x−4)2+(y−3)2=(4)2

so center is (4,3) and radius is 4.

Distance between center and given point √(4−3)2+(3+2)2=√26 which is greater than 4.

hence point lies outside the circle .

Since point lies outside of the circle there will be 2 tangents since two tangents can be drawn from external point to a circle.
Question 10
1 / -0

The number of tangents which can be drawn from the point (– 1, 2) to the circle x² + y² + 2x – 4y + 4 = 0 is

A
1

B
2

C
3

D
0
Question 11
1 / -0

Which of the following statements is true for the two circles x² + y² – 4y = 0 and x² + y² – 8y = 0?

A
They touch each other internally.

B
They touch each other externally.

C
They do not touch each other.

D
None of these
Question 12
1 / -0

If the equation x² + 2gx + 2fy + c = 0 represents a circle with x-axis as a diameter and radius a, then

A
f = 2a, g = 0, c = 3a²

B
f = 0, g = a, c = 3a²

C
f = 0, g = – 2a, c = 3a²

D
none of these

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Re-Attempt Weekly Quiz Competition

Circles Test - 2

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Circles Test - 2

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SHARING IS CARING

Question 1

circle

parabola

ellipse

hyperbola

Question 2

x2 + y2 – ax – by = 0

x2 + y2 + ax + by = 0

x2 + y2 – ax + by = 0

x2 + y2 + ax – by = 0

Question 3

π (h2 + k2 – a2)

π a2hk

π a2

None of these

Question 4

(x – 2)2 + (y – 3)2 = 8

(x – 2)2 + (y – 3)2 = 3

(x + 2)2 + (y – 3)2 = 2√2

(x – 2)2 + (y – 3)2 = 2√2

Question 5

(– 5, – 7) and 6

(– 6, – 9) and 36

(15, 4) and 6

(19, 5) and 6

Question 6

x2 + y2 + 8x – 6y + 9 = 0

x2 + y2 + 8x + 6y – 11 = 0

x2 + y2 + 8x – 6y – 9 = 0

none of these

Question 7

a2/3

2a2/3

a2/6

a2/12

Question 8

At most one

At most two

Infinite

None of these

Question 9

1

2

0

none of these

Solution

Question 10

1

2

3

0

Question 11

They touch each other internally.

They touch each other externally.

They do not touch each other.

None of these

Question 12

f = 2a, g = 0, c = 3a2

f = 0, g = a, c = 3a2

f = 0, g = – 2a, c = 3a2

none of these

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x² + y² – ax – by = 0

x² + y² + ax + by = 0

x² + y² – ax + by = 0

x² + y² + ax – by = 0

π (h² + k² – a²)

π a²hk

π a²

(x – 2)² + (y – 3)² = 8

(x – 2)² + (y – 3)² = 3

(x + 2)² + (y – 3)² = 2√2

(x – 2)² + (y – 3)² = 2√2

x² + y² + 8x – 6y + 9 = 0

x² + y² + 8x + 6y – 11 = 0

x² + y² + 8x – 6y – 9 = 0

a²/3

2a²/3

a²/6

a²/12

f = 2a, g = 0, c = 3a²

f = 0, g = a, c = 3a²

f = 0, g = – 2a, c = 3a²