2.
The diameters of two citcles touching
each other externally are 26 cm
and 14 om gespectively. Find the
distance between their contres
Answers
Answer:
Hey Mate!
Step-by-step explanation:
Let the center of the circle be (h,k).
As it touches y−axis, radius will be equal to abscission of the center Hence the equation of the circle is given by
(x−h)
2
+(y−k)
2
=h
2
x
2
+y
2
−2hx−2xy+k
2
=0
As the circle passes through (a,5a) and (4a,a), these point will satisfy.
a
2
+25a−2ah−10ka+k
2
=0⟶(2)
16a
2
+a
2
−8ah−2ka+k
2
=0⟶(3)
(3) from (2), we get
9a
2
+6ah−8ak=0
2ah=
3
1
(8ak−9a
2
)⟶(4)
Substituting this value in (2), we get.
a
2
+25a
2
−
3
1
(8ak−9a
2
)−10ka+k
2
=0
3k
2
−38ak+87a
2
=0
(k−3a)(3k−29a)=0
k=3aork=
3
29
a.
Substituting this value in (4), we get.
h=
2
5a
and
18
205
a
∴ The centers of two circles will be
(
2
5a
,3a)&(
18
205a
,
3
29a
)
Now the slope of the line joining the center (
2
5a
,3a) to the point of intersection (4a,a).
=
2
5a
−4a
3a−a
=
3
4
=m
1
Slope of the line joining (
18
205a
,
3
29a
) to the point (−4a,a).
=
18
205a
−4x
3
29
a−a
=
133
156
m
2
If the angle b/w two lines be O, then
tanθ=
1+m
1
m
2
m
1
−m
2
=
1−
3
4
×
133
156
−
3
4
−
133
156
=
9
40
θ=tan
−1
(
9
40
)