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Standard XII

Mathematics

Implicit Differentiation

The circle ...

Question

The circle $S_{1}$ has centre at $(1, 2)$ and radius $3$ ; the circle $S_{2}$ has centre at $(9, 8)$ and radius $7$ . The circles $S_{1}$ and $S_{2}$ touch at the point whose co-ordinates are:

(\begin{matrix} \frac{17}{5}, \frac{19}{5} \end{matrix})

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(\begin{matrix} \frac{33}{5}, \frac{31}{5} \end{matrix})

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(\begin{matrix} \frac{17}{10}, \frac{19}{10} \end{matrix})

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(\begin{matrix} \frac{33}{10}, \frac{31}{10} \end{matrix})

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Solution

The correct option is A $(\begin{matrix} \frac{17}{5}, \frac{19}{5} \end{matrix})$

$P (x, y) = (\begin{matrix} \frac{m x_{2} + n x_{2}}{m + n}, \frac{m y_{2} + n x}{m + n} \end{matrix})$
$= (\begin{matrix} \frac{27 + 7}{10}, \frac{24 + 14}{10} \end{matrix}) = (\begin{matrix} \frac{17}{5}, \frac{19}{5} \end{matrix})$

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Similar questions

Q. The circle

S_{1}

with centre

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

and radius

r_{1}

touches externally the circle

S_{2}

with centre

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

and radius

r_{2}

. If the tangent at their common point passes through the origin then

Q. Let

S_{1}

and

S_{2}

be two circles touching externally and having radius as

2

and

3

respectively.

S_{1}

and

S_{2}

touch a variable circle

S_{3}

internally at

A

and

B

respectively. If the tangents to

S_{3}

A

and

B

meet at

T

and

T A = 4 units

, then which of the following is/are correct?
(Here,

C_{i}

represents the centre of circle

S_{i}

)

3

circle of radii

1, 2

and

3

and centres at

A, B, C

respectively, touch each other. Another circle whose centre is

P

touches all these

3

circles externally and has radius

r

. Also

∠ P A B = θ

and

∠ P A C = α

Q. Let

S_{1}

and

S_{2}

be two circles touching externally and having radius as

2

and

3

respectively.

S_{1}

and

S_{2}

touch a variable circle

S_{3}

internally at

A

and

B

respectively. If the tangents to

S_{3}

A

and

B

meet at

T

and

T A = 4 units

, then which of the following is/are correct?
(Here,

C_{i}

represents the centre of circle

S_{i}

)

Q. Figure shown line

L = 0

which is radieal axis of

S_{1} = 0

and

S_{2} = 0

. The direct common tangent touches circle

S_{1} = 0

and

S_{2} = 0

A

and

B

respectively and cuts

L = 0

P

. Let

\frac{A r e a (Δ P A C_{1})}{A r e a (Δ P B C_{2})} = 2

and radius of

S_{2} = 0

5

, if radius of

S_{1} = 0

r

then the value of

\frac{r}{5}

is (

C_{1}

and radius of

S_{2} = 0

5

, if radius of

S_{1} = 0

r

then the value of

\frac{r}{5}

C_{1}

and

C_{2}

are centres of

S_{1} = 0

and

S_{2} = 0

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The circle S1 has centre at (1,2) and radius 3; the circle S2 has centre at (9,8) and radius 7. The circles S1 and S2 touch at the point whose co-ordinates are:

The correct option is A (175,195)P(x,y)=(mx2+nx2m+n,my2+nxm+n)=(27+710,24+1410)=(175,195)

The circle $S_{1}$ has centre at $(1, 2)$ and radius $3$ ; the circle $S_{2}$ has centre at $(9, 8)$ and radius $7$ . The circles $S_{1}$ and $S_{2}$ touch at the point whose co-ordinates are: