 Hello and welcome to the session. In this session we will discuss a question which says that find the equation of the parabola with its axis parallel to y axis and passes through the points 1 phi minus 2 8 and 3 minus 1. Now before starting the solution of this question we should know our result. And that is equation of the parabola into y axis just as the form minus alpha whole square is equal to 4 a into y minus beta the whole. So this is the parabola and its vertex are alpha beta and the coordinates of its focus are alpha as beta plus a plus square minus 2 x alpha is equal to 4 a y minus 4 a beta which further implies 4 a y is equal to x square plus alpha square minus 2 x alpha plus 4 a beta. Now dividing through x by 4 a this implies y is equal to x square by 4 a minus 2 x alpha by 4 a beta square whole upon this further implies y is equal to 1 by 4 a into x square minus by 2 a a beta plus alpha square whole upon 4 a. It will be a x square and putting this vector as b it will be plus b x y is equal to a x square plus b x plus c where a b and c are the constants whose value. Now this result will work out as a key idea. Now we will start with the solution of the parabola this one. Now using this as a key idea now let us know this as equation number 1. Now given that the parabola 1 3 minus 2 8 these values in equation number 1 we get y is equal to 3 in equation number 1 so it will become 3 is equal to a plus b and y is equal to 8 in equation number 1 we get equal to a into minus 2 square which will be b into minus 2 will be minus i is equal to minus 1 in this way it will become minus 1 is equal to a x square will become a into 3 square which will be 9 a plus b into x will be b into 3 3 b plus c. Now in equation number 2 we get in equation number 3 which implies 3 is equal to 30 minus a will be 3 a minus 2 b minus b will be minus 3 b minus 3 b equation number 5 b minus a minus b in equation number 4 which implies minus 3 is equal to 4 is equal to 8 a plus 2 b which gives minus 2 is equal to 4 a equation number 6 we get equal to minus 2 minus equal to minus 2 minus 4 a in equation number 5 we get in equation number 5 it will be 5 is equal to 3 a plus 4 a the whole which further implies is equal to 3 a plus 12 a which was which further gives minus 1 is equal to 15 a and this implies a is equal to minus 1 by 50. Now putting equal to minus 2 minus 4 into minus 1 by 15 the whole which implies b is equal to minus 1 by 15 which on solving gives b is equal to minus now we have a is equal to minus 1 by 15 2 we have c is equal to 3 minus a minus b therefore the values of b minus a minus b we get minus 1 by 5 of minus 26 by 15 c is equal to 3 plus 1 by 15 which further is 45 plus 1 in 1 into minus 1 by 15 into x square minus 26 by 15 into x which further implies is equal to minus x square minus 26 72 is equal to 0 equation and that's all for this session hope you all have enjoyed the session.