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hello,

I hope your question was ax^{2}+2hxy+by^{2} is rotated by 90^{0} about origin and after rotation what should be it's new equation.

to solve this question you must be aware of shifting of origin which says if the function is rotated by angle A then let it's new axis be X and Y such that

X=xcosA - ysinA

Y=xsinA + ycosA

putting A=900

X=-y & Y=x

now in the equation of pair of straight line replace x by Y and y by -X you will get

aY^{2} - 2hXY + bX^{2}

hence the new equation is ay^{2}-2hxy+bx^{2}

hope I answered your question

feel free to ask any doubt related to this.....