 Welcome to the session. In this session, we will discuss a question which says that, transform the following parabolas to the standard forms. x minus 5 by 2 whole square is equal to 2 into y plus 3 by 4 the whole. Second part, 3 by square plus 12x minus 18 y plus 53 is equal to 0. Now before starting the solution of this question, we should know a result. And that is to express a given equation in standard form by shifting the origin. That is when the equation of the parabola is given in a far other than the standard form. That is of the time y plus minus beta whole square is equal to lambda into x plus minus alpha the whole. This alpha whole square is equal to lambda into y plus minus beta the whole lambda alpha and beta. We will shift the origin to minus plus alpha minus plus beta by putting x is equal to x plus minus. The second part y is equal to y plus minus beta that is if the equation of the parabola is given in a far other than the standard form. That is in this form when we will shift the origin to minus plus alpha minus plus beta that means beta is positive and alpha is positive here. Then we will shift the origin to minus alpha minus beta by putting y is beta in the given equation. Negative here then x is equal to x minus alpha and y is equal to y minus beta in the given equation. And then the equation coordinate system y square is equal to lambda into capital X which is equal to 4 into lambda by 4 into capital X. V is equal to lambda into capital Y which is equal to 4 into lambda by 4 into capital Y which is the standard form of the equation of parabola. So by this method we can express the equation of parabola origin. Now this result will welcome to the key idea for solving out this question. And now we will start with the solution. Let us start with the first part. Now we have to express this equation in the standard form of the equation of parabola. Now given whole square is equal to 2 into y plus 3 by 4 the whole which is given in the key idea is negative and beta is positive. Beta that is minus 3 by 4 by putting x is equal to x to y plus 3 by 4. The equation number 1 we will put these values in equation number 1. I can say that for 1 by 4 into y which implies 1 by 2 into y parabola. That is x square is equal to 4 a y equal to 1 by 2. Now a is equal to 1 by 2 and this is in the form x square is equal to 4 a y minus 18 y plus 53 is equal to 0. In the standard form of the equation of parabola by shifting the origin. Now the given equation can be written as y is equal to minus 12 x minus 53. Now x by 3 it will give y square minus 6 y is equal to minus 53 by 3. Now completing the coefficient of y into whole square x minus 53 by 3 and 3 square is 9 minus will be 3 square which is 9. So it will be minus 9 which is equal to minus 4 x minus 53 by 3. y square minus now 6 y is equal to 3 9 can be written as 3 square is equal to minus 4 x minus 53 by 3. It is completed y minus 3 whole square is equal to minus 4 x and I am solving we get minus 26 by 3 minus 3 whole square is equal to it will be minus 4 into x plus 26. y n is equal to minus 4 into x plus 2 into 6 is 12 into 13 is 26 so it will be plus 13 that is this equation in the standard form of the equation of parabola by shifting the origin. Here beta is negative and alpha is positive beta that is 3 13 by 6 equal to y minus 3 let it be equation number 2 and is equal to minus equal to minus 4 into 1 into x which is the equation of parabola that is in the form y square is equal to minus 4 A x and here A. So this is the solution of the given question and that is all for this lecture at the session.