A circle is drawn touching the x-axis and centre at the point which is the reflection of ( a , b ) in the line y-x=0. The equation of the circle is -

Question

A circle is drawn touching the x-axis and centre at the point which is the reflection of ( a , b ) in the line y-x=0. The equation of the circle is - (A) x2+y2-2 b x-2 a y+a2=0 (B) x2+y2-2 b x-2 a y+b2=0 (C) x2+y2-2 a x-2 b y+b2=0 (D) x 2+ y 2-2 ax -2 by + a 2=0

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a6d43b234fbd5272119a7ba22b6565ce-.png" /> Reflection of point ( a , b ) on the line y=x will be (b, a) (x-b)2+(y-a)2=a2 x2+y2-2 b x-2 a y+b2=0

Q. A circle is drawn touching the $x$ -axis and centre at the point which is the reflection of $(a, b)$ in the line $y - x = 0$ . The equation of the circle is -

$x^{2} + y^{2} - 2 b x - 2 a y + a^{2} = 0$

$x^{2} + y^{2} - 2 b x - 2 a y + b^{2} = 0$

$x^{2} + y^{2} - 2 a x - 2 b y + b^{2} = 0$

$x^{2} + y^{2} - 2 a x - 2 b y + a^{2} = 0$

Reflection of point $(a, b)$ on the line
$y = x$ will be $(b, a)$
$(x - b)^{2} + (y - a)^{2} = a^{2}$
$x^{2} + y^{2} - 2 b x - 2 a y + b^{2} = 0$

Q. A circle is drawn touching the x-axis and centre at the point which is the reflection of (a,b) in the line y−x=0. The equation of the circle is -

x2+y2−2bx−2ay+a2=0

x2+y2−2bx−2ay+b2=0

x2+y2−2ax−2by+b2=0

x2+y2−2ax−2by+a2=0