IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

Sivvar

the equations given are those of a circle n a parabola as shown in the dia:

first let tangent be y= mx+c

c=1/4m if this line is tangent to the parabola..

next frm the eqn of circle we find the centre to be (0,3)..radius is root 5.

dist of centre frm tangent=radius.

usin this n eqn of tangent

(3 - 1/4 m) / ((root) (1+m²)) = (root) 5

square this..

80m⁴- 64 m²+24m -1=0;

big eqn:)....by inspection u find this root is 1/2..

then eqn of tangent is y -1/2 x - 1/2=0.

n thts the ans u gave kane..hope its clear..