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Equation of smallest circle passing through 'points of intersection of line $x + y = 1$ & circle $x^{2} + y^{2} = 9$

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Important Questions on Circle

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

Find the equation of the circle which passes through the point

(1, 2)

and the points of intersection of the circles

x^{2} + y^{2} - 8 x - 6 y + 21 = 0

and

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

HARD

Mathematics>Coordinate Geometry>Circle>Family of Circles

If a circle

C

, whose radius is

3

, touches externally the circle

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

at the point

(2, 2)

, then the length of the intercept cut by this circle

C

on the

x

-axis is equal to

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

A circle

C

touches the line

x = 2 y

at the point

(2, 1)

and intersects the circle

C_{1} : x^{2} + y^{2} + 2 y - 5 = 0

at two points

P

and

Q

such that

P Q

is a diameter of

C_{1}

. Then the diameter of

C

is :

HARD

Mathematics>Coordinate Geometry>Circle>Family of Circles

The equation of a circle passing through the point

(1, 1)

and the point of intersection of the circles

x^{2} + y^{2} + 13 x - 3 y = 0

and

2 x^{2} + 2 y^{2} + 4 x - 7 y - 25 = 0

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

The line

x = y

touches a circle at the point

(1, 1)

. If the circle also passes through the point

(1, - 3)

, then its radius is

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

The equation of the circle passing through

(1, 1)

and through the points of intersection of the circles

x^{2} + y^{2} + 13 x - 3 y = 0

and

2 x^{2} + 2 y^{2} + 4 x - 7 y - 25 = 0

HARD

Mathematics>Coordinate Geometry>Circle>Family of Circles

The equation of a circle passing through the points of intersection of the circles

x^{2} + y^{2} - 4 x - 6 y - 12 = 0, x^{2} + y^{2} + 6 x + 4 y - 12 = 0

and having radius

\sqrt{13}

EASY

Mathematics>Coordinate Geometry>Circle>Family of Circles

Let

C_{1}

and

C_{2}

be the centres of the circles

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

and

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

respectively. If

P

and

Q

are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral

P C_{1} Q C_{2}

is :

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

A circle touches the

y

-axis at the point

(0, 4)

and passes through the point

(2, 0)

. Which of the following lines is not a tangent to this circle?

HARD

Mathematics>Coordinate Geometry>Circle>Family of Circles

If a circle

C

passing through the point

(4, 0)

touches the circle

x^{2} + y^{2} + 4 x - 6 y = 12

externally at the point

(1, - 1),

then the radius of

C

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

Two circles each of radius

5

units touch each other at the point

(1, 2) .

If the equation of their common tangent is

4 x + 3 y = 10

, and

C_{1} (α, β)

and

C_{2} (γ, δ), C_{1} \neq C_{2}

are their centres, then

| (α + β) (γ + δ) |

is equal to

HARD

Mathematics>Coordinate Geometry>Circle>Family of Circles

The equation of the circle described on the chord

3 x + y + 5 = 0

of the circle

x^{2} + y^{2} = 16

as the diameter is

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

The equation of the circle passing through the points of intersection of two circles

x^{2} + y^{2} + 2 x + 3 y + 1 = 0, x^{2} + y^{2} + 4 x + 3 y + 2 = 0

and the point

(- 1, 1)

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

If a circle has its centre on the line

x - y - 1 = 0

and passes through the points of intersection of the two circles

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

and

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

then the centre of that circle is

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

Let

x^{2} + y^{2} + A x + B y + C = 0

be a circle passing through

(0, 6)

and touching the parabola

y = x^{2}

(2, 4)

. Then

A + C

is equal to _____

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

The circle passing through

(1, - 2)

and touching the axis of

x

(3, 0)

also passes through the point

HARD

Mathematics>Coordinate Geometry>Circle>Family of Circles

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:

HARD

Mathematics>Coordinate Geometry>Circle>Family of Circles

The circle passing through the intersection of the circles,

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

and

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

having its centre on the line,

2 x - 3 y + 12 = 0

, also passes through the point :

HARD

Mathematics>Coordinate Geometry>Circle>Family of Circles

The area (in sq. units) of the smaller of the two circles that touch the parabola,

y^{2} = 4 x

at the point

(1, 2)

and the

x

-axis is

MEDIUM

Mathematics>Coordinate Geometry>Circle>Family of Circles

If a circle

C

passing through the point

(4, 0)

touches the circle

x^{2} + y^{2} + 4 x - 6 y = 12

externally at the point

(1, - 1),

then the radius of

C

is:

Equation of smallest circle passing through 'points of intersection of line x+y=1 & circle x2+y2=9

Important Questions on Circle

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Equation of smallest circle passing through 'points of intersection of line $x + y = 1$ & circle $x^{2} + y^{2} = 9$