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Equation of C...

Equation of Circle with (h,k) as Center

Trending Questions

Q.

Let $c_{1} : x^{2} + y^{2} = 1; C_{2} : (x - 10)^{2} + y^{2} = 1 a n d C_{3}; x^{2} + y^{2} - 10 x - 42 y + 457 = 0$ be three circle.A circle C has been drawn to touch circles $C_{1}$ and $C_{2}$ externally and $C_{3}$ internally. Now circles $C_{1}, C_{2}$ and $C_{3}$ start rolling on the circumference of circle C in anticlockwise direction with constant speed. The centroid of the triangle formed by joining the centres of rolling circles $C_{1}, C_{2}$ and $C_{3}$ lies on

$x^{2} + y^{2} - 12 x - 22 y + 144 = 0$
$x^{2} + y^{2} - 10 x - 24 y + 144 = 0$
$x^{2} + y^{2} - 8 x - 20 y + 64 = 0$
$x^{2} + y^{2} - 4 x - 2 y - 4 = 0$

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Q. Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for

$\forall k \in I$
K < 0
0 < k < 1
For two values of k

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Q.

A pair of straight lines $x^{2} - 8 x + 12 = 0$ and $y^{2} - 14 y + 45 = 0$ are forming a square. Co-ordinates of the center of the circle inscribed in the square are

(4, 7)
(3, 6)
(4, 8)
none

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Q. The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y - 4x + 3 = 0, is

$x^{2} + y^{2} + 4 x - 10 y + 25 = 0$
$x^{2} + y^{2} - 4 x - 10 y + 25 = 0$
$x^{2} + y^{2} - 4 x - 10 y + 16 = 0$
$x^{2} + y^{2} - 14 y + 8 = 0$

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Q.

The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point

(-5, 2)
(2, -5)
(5, -2)
(-2, 5)

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Q. The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is

$(x - 5)^{2} + (y + 5)^{2} = 25$
$(x + 4)^{2} + (y + 4)^{2} = 25$
$(x - 6)^{2} + (y + 6)^{2} = 25$
$(x + 5)^{2} + (y + 5)^{2} = 25$

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Q. The equation of circle passing through (4, 5) and having the centre at (2, 2), is

$x^{2} + y^{2} + 4 x + 4 y - 5 = 0$
$x^{2} + y^{2} - 4 x - 4 y - 5 = 0$
$x^{2} + y^{2} - 4 x - 4 y + 5 = 0$
$x^{2} + y^{2} - 4 x = 13$

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Q. In the adjoining figure, two circles intersect each other at points

S

and

R

. Their common tangent

P Q

touches the circle at points

P, Q

.
Prove that,

∠ P R Q + ∠ P S Q = 180^{\circ}

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Q. The equation of the circle whose radius is 5 and which touches the circle

x^{2} + y^{2} - 2 x - 4 y - 20 = 0

externally at the point (5, 5), is

$x^{2} + y^{2} - 18 x - 16 y - 120 = 0$
$x^{2} + y^{2} + 18 x + 16 y - 120 = 0$
$x^{2} + y^{2} + 18 x - 16 y + 120 = 0$
$x^{2} + y^{2} - 18 x - 16 y + 120 = 0$

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Q. The circle

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

and hyperbola

\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1

intersect at the points

A

and

B

Equation of the circle with

A B

as its diameter is

(A) $x^{2} + y^{2} - 12 x + 24 = 0$
(B) $x^{2} + y^{2} + 12 x + 24 = 0$
(C) $x^{2} + y^{2} + 24 x - 12 = 0$
(D) $x^{2} + y^{2} - 24 x - 12 = 0$

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Q. A circle is circumscribed about an equilateral triangle

A B C

and a point

P

on the minor are joining

A

and

B

, is chosen. Let

x = P A, y = P B

and

z = P C

.(

z

is larger than both

x

and

y

.)
Statement-

1

: Each of the possibilities

(x + y)

grater than

z

, or less than

z

, is possible for some

P

.
Because
Statement-

2

: In a triangle ABC , sum of the two sides of a triangle is grater than the third and the third side is grater than the difference of the two.

Statement- $1$ - is true, Statement- $2$ - is true and Statement- $2$ - is correct explanation for Statement- $1$ .
Statement- $1$ - is true, Statement- $2$ is true and Statement- $2$ is $N O T$ the correct explanation for Statement- $1$ .
Statement- $1$ is true , Statement- $2$ are false
Statement- $1$ are false , Statement- $2$ is true

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Q. The coordinates of the point on the parabola

x^{2} = 8 y

, whose distance from the circle

(x - 4)^{2} + (y - 2)^{2} = 1

is minimum is

$3$
$2$
$0$
$5$

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Q. The equation of circle with centre

(- 4, 3)

and touching the circle

x^{2} + y^{2} = 1

, is

$x^{2} + y^{2} + 8 x - 6 y + 9 = 0$
$x^{2} + y^{2} + 8 x + 6 y - 11 = 0$
$x^{2} + y^{2} + 8 x + 6 y - 9 = 0$
$N o n e o f t h e s e$

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Q. If the area of a circle is halved when its radius is decreased by n, then the radius is equal to

$n (2 + \sqrt{2})$
$n (\sqrt{2} - 1)$
$n (3 - \sqrt{2})$
$n \sqrt{2}$

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Q. A plane passes through a fixed point

(a, b, c)

. The locus of the foot of the perpendicular to it from the origin is the sphere

$x^{2} + y^{2} + z^{2} - 2 a x - 2 b y - 2 c z = 0$
$x^{2} + y^{2} + z^{2} - a x - b y - c z = 0$
$x^{2} + y^{2} + z^{2} - 4 a x - 4 b y - 4 c z = 0$
none of these

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Q. Equation of a circle whose centre is origin and radius is equal to the distance between the lines x = 1 and x = -1 is

$x^{2} + y^{2} = 1$
$x^{2} + y^{2} = \sqrt{2}$
$x^{2} + y^{2} = 4$
$x^{2} + y^{2} = - 4$

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Q. The nearest point of the circle

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

from

(- 5, 4)

is

(-1, 2)
(1, 1)
(-1, 1)
(-2, 2)

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Q. The points of intersection of the line

4 x - 3 y - 10 = 0

and the circle

x^{2} + y^{2} - 2 x + 4 y - 20 = 0

are...................and....................

$(- 2, - 4)$
$(- 2, - 6)$
$(2, 2)$
$(4, 2)$

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