Question

find the equation of the circle with centre (h,k)and touching (1) x-axis (2)y-axis

Answer 1

Hi Mate!!

1). Equation of circle touching x - axis is

( x - h )² + ( y - k )² = k²

2) Equation of circle touching y -axis is

( x - h )² + ( y - k )² = h²

Answer 2

1) x-axis, $(x-h)^{2} +y^{2} =a^{2}$

2) y-axis,$x^{2} +(y-k)^{2} =a^{2}$

Step-by-step explanation:

To find, the equation of the circle with centre (h, k)and touching 1) x-axis

2) y-axis

We know that,

The equation of a circle with centre at (h, k) and radius equal to a

= $(x-h)^{2} +(y-k)^{2} =a^{2}$

1) x-axis

Puy k = 0, we get

The equation of the circle with centre (h, k)and touching x-axis

$(x-h)^{2} +(y-0)^{2} =a^{2}$

$(x-h)^{2} +y^{2} =a^{2}$

2) y-axis

Puy h = 0, we get

The equation of the circle with centre (h, k)and touching y-axis

$(x-0)^{2} +(y-k)^{2} =a^{2}$

$x^{2} +(y-k)^{2} =a^{2}$