 Hello and welcome to the session. In this session we will discuss a question which says that I am the asymptote of the hyperbola x square over 9 minus y square over 4 is equal to 1. Now before starting the solution of this question we should know a result. And that is a asymptote, a straight line which tends to touch the given pair at infinity. The asymptote which is neither parallel to x axis nor parallel to y axis is called an oblique asymptote of the power. Now this result will work out as a key idea for solving out this question. And now we will start with the solution. Now we have to find the asymptotes of this given hyperbola. Now we know that asymptote is a line which tends to touch the curve at infinity. So let y is equal to mx plus c be the asymptote of the given hyperbola over 9 minus y square over 4 is equal to 1. Now let this be equation number 1. So putting y is in equation number 1 we get over 9 minus mx plus c per square over 4 is equal to 1. Which further implies minus 9m square x square minus 9c square is equal to, on solving this further implies 9m square minus 4 the whole into x square minus 18 the whole is equal to 0. Now let this be equation number 2. Now if the line to mx plus c is an asymptote to the given hyperbola it touches the hyperbola that roots this equation that is of equation number 2 must be infinite. Now this is a quadratic equation in x. So for both fields to be infinite the coefficient of x square that is a should be equal to 0 and the coefficient of x which is b should be equal to 0. Therefore m square minus 4 is equal to 0 minus 18mc is equal to 0 which implies m square is equal to 4 by 9 which further implies m is equal to plus minus 2 by 3 c is equal to 0. Now putting the values asymptote which we have taken as y is equal to mx plus c we get y is equal to plus minus 2 by 3 into x plus 0 which further implies y is equal to plus minus 2 by 3 into x. Now the equations of the given hyperbola now here considering the positive sign we will get the equation of one asymptote that will be 2x minus 3y is equal to 0 and now considering the negative sign here and further solving we will get the second equation that is 3y is equal to 0. So these are the equations of the asymptotes of the given equation and that's all for this session. Hope you all have enjoyed the session.