Show that the families of curves defined by the eqn y=ax, y²+x²=c² are perp for

(a)a=2,c=4 (b)a=-2,c=3 (c) a=3,c=2 (d) a=3,c=-2

hi Tushar, y^2+x^2=c^2 is a circle that has its center as the origin and the line y = ax is straight line that passes through the centre. the line of this family will always represent a radius of the circle. it is known that the radius is always perpendicular to a tangent according to the definition of tangents, hence this family of lines is always normal to the circle irrespective of the values of c and a (a just defines the slope of the line and c is the length of the radius of the circle), so these two families of curve are perpendicular for all values of a & c. Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best . Regards, Askiitians Experts Pratham IIT - Delhi