First slide

Definition of a circle

Question

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

Moderate

A

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

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

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

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

Solution

$The reflection of (a, b) in the line y = x is (b, a)$
$\begin{array}{l} : Equation of circle having centre at (b, a) and touching x-axis is (x - b)^{2} + (y - a)^{2} = a^{2} \\ \Rightarrow x^{2} + b^{2} - 2 b x + y^{2} + a^{2} - 2 a y = a^{2} \\ \Rightarrow x^{2} + y^{2} - 2 b x - 2 a y + b^{2} = 0 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App