A circle is drawn touching the x-axis. with its centre at the point of reflection of (m, n) on the line y-x=0. Then the equation of the circle is

Question

A circle is drawn touching the x-axis. with its centre at the point of reflection of (m, n) on the line y-x=0. Then the equation of the circle is (A) x2+y2-2 m x-2 n y+ m2=0 (B) x2+y2-2 m x+2 n y+ m2=0 (C) x2+y2+2 n x-m y-n2=0 (D) x2+y2-2 n x-m y +n2=0

Tardigrade Admin · Accepted Answer

The point of reflection of (m, n) on the line y-x=0 is (n, m), so equation of circle having centre (n, m) and let radius r is (x-n)2+(y-m)2=r2 ldots . . (i) ∵ Circle (i) touches the X-axis, so r=m So, equation of required circle is (x-n)2+(y-m)2=m2 or x2+y2-2 n x-2 m y+ n2=0

Q. A circle is drawn touching the $x$ -axis. with its centre at the point of reflection of $(m, n)$ on the line $y - x = 0$ . Then the equation of the circle is

$x^{2} + y^{2} - 2 m x - 2 n y + m^{2} = 0$

$x^{2} + y^{2} - 2 m x + 2 n y + m^{2} = 0$

$x^{2} + y^{2} + 2 n x - m y - n^{2} = 0$

$x^{2} + y^{2} - 2 n x - m y + n^{2} = 0$

Q. A circle is drawn touching the x-axis. with its centre at the point of reflection of (m,n) on the line y−x=0. Then the equation of the circle is

x2+y2−2mx−2ny+m2=0

x2+y2−2mx+2ny+m2=0

x2+y2+2nx−my−n2=0

x2+y2−2nx−my+n2=0

The point of reflection of (m,n) on the line y−x=0 is (n,m), so equation of circle having centre (n,m) and let radius r is (x−n)2+(y−m)2=r2….. (i) ∵ Circle (i) touches the X-axis, so r=m So, equation of required circle is (x−n)2+(y−m)2=m2 or x2+y2−2nx−2my+n2=0

Q. A circle is drawn touching the $x$ -axis. with its centre at the point of reflection of $(m, n)$ on the line $y - x = 0$ . Then the equation of the circle is

$x^{2} + y^{2} - 2 m x - 2 n y + m^{2} = 0$

$x^{2} + y^{2} - 2 m x + 2 n y + m^{2} = 0$

$x^{2} + y^{2} + 2 n x - m y - n^{2} = 0$

$x^{2} + y^{2} - 2 n x - m y + n^{2} = 0$