Question

The number of common tangents to the circles: x(x-4)+ yly-6)=12 and x(x+6)+ yl y+ 18)=-26 is​

Answer 1

Answer:

Solution

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Correct option is

B

(6,−2)

Circle touches internally

C

1

(0,0):r

1

=2

C

2

:(−3,−4);r

2

=7

C

1

C

2

=∣r

1

−r

2

∣

S

1

−S

2

=0 ⇒ equation of common tangent

6x+8y−20=0

3x+4y=10

(6,−2) satisfies the equation.

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Answer 2

Step-by-step explanation:

For the first circle,

C

1

:(2,3)

R

1

=

2

2

+3

2

+12

=5

For the second circle,

C

2

:(−3,−9)

R

2

=

3

2

+9

2

−26

=8

Distance between C

1

and C

2

=

5

2

+12

2

=13

R

1

+R

2

=13

Hence, the circles touch each other externally.

For such circles, there are three common tangents.

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