Question

Find the equation of a circle.
(i) Which touches both the axes at a distance of $6$ units from the origin.
(ii) Which touches x-axis at a distance $5$ from the origin and radius $6$ units.
(iii) Which touches both the origin, radius $17$ and ordinate of the centre is $-15$.
(iv) Passing through the origin, radius $17$ and ordinate of the centre is $-15$.

Answer 1

(i) R.E.F image

Center : (6,6)

radius = 6 units

$\therefore E{q}^n(x-6{)}^2+(y-6{)}^2=36.$

(ii) R.E.F image

Center : (5,6)

radius : 6 units

$E{q}^n:(x-5{)}^2+(y-6{)}^2=36.$

(iii) R.E.F image

$x=\sqrt{{17}^2-{15}^2}=8$

Center : (-8,-15)

radius : 17

$E{q}^n:(x+8{)}^2+(y+15{)}^2={17}^2$ } same equation for (iv).