Question
Find the equation of circle whose radius is 5 and which touches the circle x2+y2−2x−4y−20=0 at the point (5, 5).
Answer: Option A
:
A
The given circle is x2+y2−2x−4y−20=0 with centre (1, 2) and radius = √1+4+20=5.
And required circle has radius 5 hence circles touch each other externally.
Since point of contact is P(5, 5).
P is the mid point of C1 and C2, let co – ordinate of centre C2 is (h, k) then
1+h2=5;h=9
2+k2=5; k = 8
And, Equation of required circle is (x−9)2+(y−8)2=52
x2+y2−18x−16y+120=0; Option(a)
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:
A
The given circle is x2+y2−2x−4y−20=0 with centre (1, 2) and radius = √1+4+20=5.
And required circle has radius 5 hence circles touch each other externally.
Since point of contact is P(5, 5).
P is the mid point of C1 and C2, let co – ordinate of centre C2 is (h, k) then
1+h2=5;h=9
2+k2=5; k = 8
And, Equation of required circle is (x−9)2+(y−8)2=52
x2+y2−18x−16y+120=0; Option(a)
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