 Hello and welcome to the session. In this session we will discuss a question which says that find the length of the intercepts of the circle x square plus y square minus 8x minus 7y plus 12 is equal to 0 on the axis of coordinates. Now before starting the solution of this question we should know a result and that is for the general equation of circle which is x square plus y square plus 2gx plus 2y plus c is equal to 0. Now let us know this equation as equation number 1 for x intercept put y is equal to 0 in equation number 1 this equation will give x square plus 2gx plus c is equal to 0. Now this is a quadratic equation in x so solving let us name it as 2. So solving 2 we get two values of x. Now x intercept will be equal to difference of the two values of x. Similarly we can find y intercept by putting x is equal to 0 in 1. So this result will work out as a key idea for solving out this question. We will start with the solution. Now in the question equation of the circle is given to us so given the equation of circle as x square plus y square minus 8x minus 7y plus 12 is equal to 0. Now using the result which is given in the key idea for x intercept put y is equal to 0 in the equation of circle. So let us name this as 1 and for x intercept putting y is equal to 0 in 1 we get x square minus 8x plus 12 is equal to 0. Now this is a quadratic equation in x so solving this by splitting the middle term it will be x square minus 2x minus 6x plus 12 is equal to 0. This implies into x minus 2 the whole minus 6 into x minus 2 the whole is equal to 0. Which implies x minus 2 the whole into x minus 6 the whole is equal to 0. Now putting each factor into 2 and x is equal to 6. Now the two values of x so here length of x intercept is equal to difference which are 2 and 6. So it will be equal to 6 minus 2 which is further equal to 4. Now for finding y intercept put x is equal to 0 in the equation of circle. So we have this as equation number 1 which is the equation of the circle. So for y intercept equal to 0 in 1 y square minus 7y plus 12 is equal to 0. Now this is a quadratic equation in y so solving this by splitting the middle term it will be y square minus 3y minus 4y plus 12 is equal to 0 which further implies y minus 3 the whole minus 4 into y minus 3 the whole is equal to 0. Which implies y minus 3 the whole into y minus 4 the whole is equal to 0. Now putting 2 to 3 and y is equal to 4. Now length of the y intercept will be equal to difference of the two values of y which are 3 and 4. So it will be equal to 4 minus 3 which is equal to 1 is equal to 4 length of the y intercept is equal to 1. This is the solution of the given question and that is all for this session. Hope you all have enjoyed this session.