If `r_1 and r_2` be the length sof perpendicular chords of a parabola `y^2 = 4x` through its vertex, then `(r_1 r_2)^(4/3)/(r_1^(2/3) + r_2^(2/3) =`

Show that if r_1 and r_2 be the lengths of perpendicular chords of a parabola drawn through the vertex, then (r_1 r_2)^(4/3) = 16a^2 (r_1^(2/3) + r_2^(2/3))

A and B are two points on the parabola y^(2) = 4ax with vertex O. if OA is perpendicular to OB and they have lengths r_(1) and r_(2) respectively, then the valye of (r_(1)^(4//3)r_(2)^(4//3))/(r_(1)^(2//3)+r_(2)^(2//3)) is

Prove that (r_1-r)(r_2-r)(r_3-r)=4R r^2

(r_(2)+r_(3))sqrt((r r_(1))/(r_(2)r_(3)))=

Prove that : 1/(r_1)+1/(r_2)+1/(r_3)=1/r

Show that (r_(1)+ r _(2))(r _(2)+ r _(3)) (r_(3)+r_(1))=4Rs^(2)

If r_(1) and r_(2) be the maximum and minimum radius of the circle which pass through the point (4, 3) and touch the circle x^(2)+y^(2)=49 , then (r_(1))/(r_(2)) is …….

If r_(1) and r_(2) be the maximum and minimum radius of the circle which pass through the point (4, 3) and touch the circle x^(2)+y^(2)=49 , then (r_(1))/(r_(2)) is …….

Prove that : (r_1+r_2) tan (C )/(2) = (r_3- r) cot ( C)/(2) = c

If r_(1), r_(2), r_(3) are radii of the escribed circles of a triangle ABC and r it the radius of its incircle, then the root(s) of the equation x^(2)-r(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1))x+(r_(1)r_(2)r_(3)-1)=0 is/are :