 Hello and welcome to the session. In this session we will discuss a question which says that find the equation of the circle which tells you the y-axis at a distance plus 4 from the origin and cuts off an intercept silk from the x-axis. Now before starting the solution of this question, we should know what is out. And that is the standard form of equation of circle is h whole square plus y minus k whole square is equal to r square where the coordinates of center r and the radius of the circle is r. Now this result will work out as a key idea for solving out this question with the solution. This is the circle with center c which touches the line which is 4 units from the origin that means it was equal to 4 units and also it cuts off an intercept of 6 from the x-axis which means bd is equal to 6. So taken the circle with center c and the circle with center c the y-axis bd is equal to so this implies cn is perpendicular, perpendicular to the circle. This is the perpendicular from the center of the circle which is c. That means cn is perpendicular to the curve bd from this cn bisects b bisects bd therefore bn is equal to md is equal to half bd. This implies bn is equal to md is equal to half here bd is equal to 6. So it will be 1 by 2 into 6 which further implies bm is equal to md is equal to 3 also oa is equal to 4. Now join vc we are getting a right angle bnc in which cn is equal to 4 and bnc is equal to bn square plus nc square. This implies p will be equal to 9 plus 16 which is 4. We have bc square is equal to 25 which further implies that the circle which is bc is equal to 5 of the circle we are therefore because this circle also 5 is equal to ac which implies is equal to 4. So the coordinates of center c that is the x coordinate of center c will be equal to o1 which is 5 and y coordinate of center c will be equal to nc which is 4. So the coordinates of center are the coordinates of center c. Now to find out the equation of the circle we will use this result. The equation of the required circle center 5 4 and radius is y minus 4 whole square is equal to 5 square which is x minus h whole square plus y minus k whole square is equal to r square. This implies x square plus 25 plus y square plus 16 minus 8 y is equal to 25. x square plus y square minus 10 x minus 8 y plus 25 plus 16 minus 25 is equal to 0. This further implies x square plus y square minus 10 x minus 8 y times will be cancelled with each other so it will be plus 16 is equal to 0. The equation of the required circle is a given question and that's all for the session. Hope you all have enjoyed the session.