Doubt from circles

Question no 14 i am not able to understand how to find normal by not using calculus using circles theory

as the normal of a circle always passes through the centre the required line should pass through (0,0) and the given point

Ok thanks

In Example 97 i am asking a question that whenever we deal with equation of circles we first make coefficents of x^2 and y^2 =1 so that we dont make any mistake in calculation but in this example of family of circles why didn't they do it will the answer would have been same if we had reduced it