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Grade: 12


Show that the families of curves defined by the eqn y=ax, y 2 +x 2 =c 2 are perp for (a)a=2,c=4 (b)a=-2,c=3 (c) a=3,c=2 (d) a=3,c=-2

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

11 years ago

Answers : (1)

Pratham Ashish
17 Points
							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.

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Askiitians Experts Pratham
 IIT - Delhi  

11 years ago
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