Math, asked by adityapundir2016, 4 months ago

equation of a circle passing through the point 1 2 and 3 4 and touching the line 3 x + y - 3 equals to zero is​

Answers

Answered by DikshithP
2

Answer:

Circle (1,2) and (3,4)−3x+y−3=0⇒(0,1)(1,0)

Let (x,y) be centre of circle ⇒ Radius is equal both points.

(x+1)

2

+(y−2)

2

=

(x−3)

2

(y−2)

2

....(1)

x

2

+1−2x+y

2

+4−4y=x

2

+9−6x+y

2

+16−8y

−20+4x+4y=0⇒x+y=5⇒y=5−x......(2)

distance from center of circle is same as radius.

(3)

2

+(1)

2

∣3x+y−3∣

=

10

∣3x+5−x−3∣

=

10

∣2x+2∣

....(3)

Substituting (2) in (1)4 equality to 3

(x−1)

2

+(3−x)

2

=

10

∣2x+2∣

⇒(x−1)

2

+(3−x)

2

=

10

(2x+2)

2

x

2

+1−2x+9+x

2

−6x=4x

2

+4

10

x

16x

2

−88x+96=0

Solving form =

2a

−b±

b

2

−4ac

=

2×16

88+±

(88)

2

−4×16×96

=

32

88±40

x

1

=

32

86+40

,x

2

=

32

88−40

x

1

=4,x

2

=1.5

Substituting x

1

and x

2

in (2) y

1

=1,y

2

=3.5

we get two circle with center (4,1) and (1.5,3.5)

Radius of circle C

1

=(4−1)

2

+(3−4)

2

=

10

C

2

=(1.5−1)

2

+(3−1.5)

2

=

2.5

C

1

⇒(x−y)

2

+(y−1)

2

=10C

2

⇒(x−1.5)

2

+(y−3.5)

2

=2.5

Step-by-step explanation:

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