Equation of F...

Equation of Family of Circles Passing through Two Points

Trending Questions

Q. Let

S_{1} : x^{2} + y^{2} = 9

and

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

. Then the locus of center of a variable circle

S

which touches

S_{1}

internally and

S_{2}

externally always passes through the points:

$(\frac{1}{2}, \pm \frac{\sqrt{5}}{2})$
$(2, \pm \frac{3}{2})$
$(1, \pm 2)$
$(0, \pm \sqrt{3})$

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Q. If two circles

x^{2} + y^{2} + 2 g x + 2 f y = 0

and

x^{2} + y^{2} + 2 g_{1} x + 2 f_{1} y = 0

touch each other, then

$f_{1} g = f g_{1}$
$f f_{1} = g g_{1}$
$f^{2} + g^{2} = f_{1}^{2} + g_{1}^{2}$
None of these

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Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1.
Show that there are two such circles.

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Find the equation of circle circumscribing the quadrilateral formed by four lines $3 x + 4 y - 5 = 0$ , $4 x - 3 y - 5 = 0$ , $3 x + 4 y + 5 = 0$ and $4 x - 3 y + 5 = 0$

$x^{2} + y^{2} = 0$
$x^{2} + y^{2} = 2$
$x^{2} + y^{2} = 25$
$x^{2} + y^{2} = 4$

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Q. In the given figure, if

A_{1}

is the area of the

Δ A O B

and

A_{2}

is the area of the parabolic region

A O B

with

x -

axis, then the ratio

\frac{A_{1}}{A_{2}}

is equal to

$\frac{1}{2}$
$\frac{3}{2}$
$\frac{3}{4}$
$\frac{2}{3}$

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Q. If ‘

A_{i}

’ is the area bounded by bounded by

| x - a_{i} | + | y | = b_{i}, i ϵ N, w h e r e a_{i + 1} = a_{i} + \frac{3}{2} b_{i} a n d b_{i + 1} = \frac{b_{i}}{2}, a_{1} = 0, b_{1} = 32

then

$A_{3} = 128$
$A_{3} = 256$
${lim}_{n \to \infty} \sum_{i = 1}^{a} A i = \frac{8}{3} (32)^{2}$
${lim}_{n \to \infty} \sum_{i = 1}^{a} A i = \frac{4}{3} (16)^{2}$

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Find the equation of circle circumscribing the quadrilateral formed by four lines $3 x + 4 y - 5 = 0$ , $4 x - 3 y - 5 = 0$ , $3 x + 4 y + 5 = 0$ and $4 x - 3 y + 5 = 0$

x² + y² = 0
x² + y² = 25
x² + y² = 2
x² + y² = 4

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The centre of the circle passing through $(0, 0)$ and $(1, 0)$ and touching the circle $x^{2} + y^{2} = 9$ can be

$(\frac{1}{2}, \frac{1}{2})$
$(\frac{1}{2}, - \sqrt{2})$
$(\frac{3}{2}, \frac{1}{2})$
$(\frac{1}{2}, \frac{3}{2})$

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Q. Find the centre and radius of the circle

2 x^{2} + 2 y^{2} = 3 x - 5 y + 7

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Q. For the two circles

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

and

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

there is/are

One pair of common tangents
Only one common tangent
No common tangent
Three common tangents

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Find the equation of circle circumscribing the quadrilateral formed by four lines $3 x + 4 y - 5 = 0$ , $4 x - 3 y - 5 = 0$ , $3 x + 4 y + 5 = 0$ and $4 x - 3 y + 5 = 0$

$x^{2} + y^{2} = 0$
$x^{2} + y^{2} = 2$
$x^{2} + y^{2} = 25$
$x^{2} + y^{2} = 4$

View Solution