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    The first thing to do when finding the normal line is we have to find the derivative so that we can find the slope. And then the normal line is perpendicular. So we're going to take the derivative of the original equation. Derivative of X ^2 is going to be two XDXDX, the derivative of two XY. We have to use the product rule. So the two times the derivative of the X times the Y + 2 X times the derivative of the Y minus the derivative of three y ^2, which is 6 YDYDX equaling the derivative of a constant 0. So here we're going to get 2X plus 2 * 1 times DX DX, which is really just one times y + 2 XDYD X -, 6 YDYDX equaling 0. I'm going to take everything without a DYDX to one side. So remember this DXDX here is really just one so -2 X -2 Y to the other side. I'm going to factor out of DYDX. So we got we get the quantity 2 X -6 Y divide each side. So we get DYDX by itself so that over two X -, 6 Y divide everything through by two negative X -, y / X -, 3 Y. Now they gave us a .33. So we're going to put in the .33 X is 3 and Y is 3. Simplifying that up, we get the derivative or the slope at the .33 being one. So the normal line has a slope of -1. So if we stick in y - 3 equal -1 X -3, that gives us our normal line of Y equal negative X + 6. Now we want to know where the line is intersects the curve. So I'm going to put that Y equal negative X + 6 into the original curve equation. X ^2 + 2 X times negative X + 6 -, 3 times the quantity negative X + 6 ^2 equaling 0. Doing a lot of algebra, foil it out distributed out combine like terms factor. We get X equal 3 and X equal 9. If we know X is 3 and X is 9, then we're going to stick those into the normal line equation because we want the point on the normal line that intersects the curve. So technically we could have put it back in the curve, but that would have been much more complex. So when I stick in three, we get -3 + 6 is 3, and that was already given. And if we read the directions, it says at what other point. So now when we stick in the nine -9 + 6 is -3. So the point X is 9 Y is -3.