Question

The equation of a circle with the
center (2, - 3) and touching the X -
axis is, * ​

Answer 1

Step-by-step explanations. The equation of circle is x

The equation of circle is x 2

The equation of circle is x 2 +y

The equation of circle is x 2 +y 2

The equation of circle is x 2 +y 2 +2gx+2fy+c=0

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0The equation touches X axis ⇒g

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0The equation touches X axis ⇒g 2

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0The equation touches X axis ⇒g 2 =c⇒c=4

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0The equation touches X axis ⇒g 2 =c⇒c=4So the required equation of circle is x

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0The equation touches X axis ⇒g 2 =c⇒c=4So the required equation of circle is x 2

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0The equation touches X axis ⇒g 2 =c⇒c=4So the required equation of circle is x 2 +y

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0The equation touches X axis ⇒g 2 =c⇒c=4So the required equation of circle is x 2 +y 2

The equation of circle is x 2 +y 2 +2gx+2fy+c=0The center of circle is (−g,−f) comparing it with (−2,3)⟹g=2,f=−3The equation with center (−2,3) is x 2 +y 2 +4x−6y+c=0The equation touches X axis ⇒g 2 =c⇒c=4So the required equation of circle is x 2 +y 2 +4x−6y+4=0

Answer 2

co-ordinates of center = (2,-3)

let the co- ordinates of the required point be = (x,0)

using distance formula.

√(x-2)^2 + (0+3)^2 ( square root over everything)

x^2-4x + 4 + 9

= x^2 -4x +13