Consider a family of circles which are passing through the point $$($$– $$1$$, $$1)$$ and are tangent to $$x-axis$$. If (h$$, $$k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval

Question

Consider a family of circles which are passing through the point $$($$– $$1$$, $$1)$$ and are tangent to $$x-axis$$. If (h$$, $$k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval

Infinity Learn · Accepted Answer

Equation of the circle with centre (h$$, $$k) and touching $$x-axis$$ is                  (x$$−$$h)2+(y$$−$$k)2=k2$$   which passes through $$($$– $$1$$, $$1)    if              $$h2+2h$$−$$2k+2=0or$$ if        $$(h+1)2=2k$$−$$1For$$ real values of h,$$2k$$−$$1$$≥$$0$$.⇒       k≥$$1/2$$

Consider a family of circles which are passing through the point $(- 1, 1)$ and are tangent to $x -$ axis. If $(h, k)$ are the coordinates of the centre of the circles, then the set of values of $k$ is given by the interval

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Consider a family of circles which are passing through the point (– 1, 1) and are tangent to x-axis. If (h, k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval

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Consider a family of circles which are passing through the point $(- 1, 1)$ and are tangent to $x -$ axis. If $(h, k)$ are the coordinates of the centre of the circles, then the set of values of $k$ is given by the interval