A region in the x y -plane is bounded by the curve y = 25 - x 2 and the line y = 0 . If the point ( a , a + 1 ) lies in the interior of the region, then

a ∈ ( - ∞ , - 1 ) ∪ ( 3 , ∞ )

EASY

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A square $A B C D$ is inscribed in a circle of radius $4$ . A point $P$ moves inside the circle such that $d (P, AB) \leq \min [d (P, B C), d (P, C D), d (P, D A)]$ , where $d (P, A B)$ denotes the distance of the point $P$ from the line $A B$ . The area of the region covered by the point $P$ is equal to

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Important Questions on Circle

MEDIUM

Mathematics>Coordinate Geometry>Circle>Circle and a Point

The ratio of the largest and shortest distances from the point

(2, - 7)

to the circle

x^{2} + y^{2} - 14 x - 10 y - 151 = 0

EASY

Mathematics>Coordinate Geometry>Circle>Circle and a Point

Given the ellipse

(E) 4 x^{2} + 9 y^{2} - 36 = 0,

the circle

(C) x^{2} + y^{2} - 9 = 0

and two points

A (1, 2), B (2, 1),

which of the following is correct?

MEDIUM

Mathematics>Coordinate Geometry>Circle>Circle and a Point

The set of values of

k

for which the circle

C : 4 x^{2} + 4 y^{2} - 12 x + 8 y + k = 0

lies inside the fourth quadrant and the point

(1, - \frac{1}{3})

lies on or inside the circle

C

HARD

Mathematics>Coordinate Geometry>Circle>Circle and a Point

If the area of an equilateral triangle inscribed in the circle

x^{2} + y^{2} + 10 x + 12 y + c = 0

27 \sqrt{3} sq . units,

then

c

is equal to:

MEDIUM

Mathematics>Coordinate Geometry>Circle>Circle and a Point

A region in the

x y

-plane is bounded by the curve

y = \sqrt{25 - x^{2}}

and the line

y = 0

. If the point

(a, a + 1)

lies in the interior of the region, then

MEDIUM

Mathematics>Coordinate Geometry>Circle>Circle and a Point

Let the point

(p, p + 1)

lie inside the region

E = \{(x, y) : 3 - x \leq y \leq \sqrt{9 - x^{2}}, 0 \leq x \leq 3\} .

If the set of all values of

p

is the interval

(a, b),

then

b^{2} + b - a^{2}

is equal to

________.

EASY

Mathematics>Coordinate Geometry>Circle>Circle and a Point

(2, a)

does not lie outside the circles

x^{2} + y^{2} = 13

and

x^{2} + y^{2} + x - 2 y = 14,

then

a

lies in

EASY

Mathematics>Coordinate Geometry>Circle>Circle and a Point

If the lines

3 x - 4 y + 4 = 0

and

6 x - 8 y - 7 = 0

are tangents to a circle, then radius of the circle is

HARD

Mathematics>Coordinate Geometry>Circle>Circle and a Point

The interval of

a

for which the point

(\sqrt{2} a, a + 2)

will be an interior point of the smaller region bounded by the circle

x^{2} + y^{2} = 8

and the parabola

x^{2} = 4 y

MEDIUM

Mathematics>Coordinate Geometry>Circle>Circle and a Point

Let the circle

S : 36 x^{2} + 36 y^{2} - 108 x + 120 y + C = 0

be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines,

x - 2 y = 4

and

2 x - y = 5

lies inside the circle

S,

then:

HARD

Mathematics>Coordinate Geometry>Circle>Circle and a Point

If the incentre of an equilateral triangle is

(1, 1)

and the equation of its one side is

3 x + 4 y + 3 = 0

, then the equation of the circumcircle of this triangle is:

HARD

Mathematics>Coordinate Geometry>Circle>Circle and a Point

If a point

P (0, - 2)

and

Q

is any point on the circle,

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

, then the maximum value of

{(P Q)}^{2}

HARD

Mathematics>Coordinate Geometry>Circle>Circle and a Point

In a circle of radius

17 c m,

two parallel chords are drawn on opposite side of a diameter. The distance between the chords is

23 c m .

If the length of one chord is

16 c m,

then the length of the other chord is

EASY

Mathematics>Coordinate Geometry>Circle>Circle and a Point

Let

P (a_{1}, b_{1})

and

Q (a_{2}, b_{2})

be two distinct points on a circle with center

C (\sqrt{2}, \sqrt{3})

. Let

O

be the origin and

O C

be perpendicular to both

C P

and

C Q

. If the area of the triangle

O C P

\frac{\sqrt{35}}{2}

, then

a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2}

is equal to __________

MEDIUM

Mathematics>Coordinate Geometry>Circle>Circle and a Point

Let

C

be the circle with center at

(1, 1)

and radius

= 1

. If

T

is the circle centered at

(0, y)

, passing through the origin and touching the circle

C

externally, then the radius of

T

is equal to

HARD

Mathematics>Coordinate Geometry>Circle>Circle and a Point

The radius of the circle

2 x^{2} + 2 y^{2} - 3 x + 2 y - 1 = 0

is _________ units.

EASY

Mathematics>Coordinate Geometry>Circle>Circle and a Point

If the coordinates of one end of a diameter of the circle

x^{2} + y^{2} - 8 x - 4 y + c = 0

are

(- 3, 2)

, then the coordinates at the other end are

HARD

Mathematics>Coordinate Geometry>Circle>Circle and a Point

The point

(- 15, 21)

lies

MEDIUM

Mathematics>Coordinate Geometry>Circle>Circle and a Point

The point

([P + 1], [P])

(where,

[x]

is the greatest integer function) lying inside the region bounded by the circle

x^{2} + y^{2} - 2 x - 15 = 0

and

x^{2} + y^{2} - 2 x - 7 = 0

, then

MEDIUM

Mathematics>Coordinate Geometry>Circle>Circle and a Point

If the point

(1, 4)

lies inside the circle

x^{2} + y^{2} - 6 x + 10 y + p = 0

and the circle does not touch or intersect the coordinate axes, then the set of all possible values of

p

is the interval

A square ABCD is inscribed in a circle of radius 4. A point P moves inside the circle such that dP,AB≤min dP,BC,dP,CD,dP,DA, where dP,AB denotes the distance of the point P from the line AB. The area of the region covered by the point P is equal to

Important Questions on Circle

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