Find the equation of the circle whose centre lies
touching the Y-axis.
radius is 5 units.
Find the equation of the circle whose center lies on the positive direction of y axis at a distance 6 units from the origin and whose radius is 4 units.
Find the equation of the circle which touches X axis at a distance 5 units from the origin and radius 6 units.
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Step-by-step explanation:
Given a circle of radius r=5
Given center lies on x-axis.
So, let the center be (h,0)
Equation of circle is
(x−h)
2
+y
2
=25 ....(1)
Since, it passes through (2,3)
⇒(2−h)
2
+3
2
=25
⇒(2−h)
2
=16
⇒2−h=±4
⇒h=−2,h=6
When h=−2, the equation of circle is
(x+2)
2
+y
2
=25
⇒x
2
+4x+4+y
2
=25
⇒x
2
+y
2
+4x−21=0
When h=6, the equation of circle is
(x−6)
2
+y
2
=25
⇒x
2
−12x+36+y
2
=25
⇒x
2
+y
2
−12x+11=0
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