The equation of the straight lines which are both tangent and normal to the curve `27x^(2)=4y^(3)` are
A
`x= pm sqrt2(y-2)`
B
`x=pm sqrt3(y-2)`
C
`x=pmsqrt2(y-3)`
D
`x=pmsqrt3(y-3)`
Text Solution
Verified by Experts
The correct Answer is:
A
`x=2t^(3), y=3t^(2)` `therefore" tangent at t is "x=yt=-t^(3)` and normal at `t_(1)` is, `xt_(1)+y=2t_(1)^(4)+3t_(1)^(2)` Since both equation represent same straight line, `(1)/(t_(1))=-t=(-t^(3))/(2t_(1)^(4)+3t_(1)^(2))` `rArr" "t^(6)-3t^(2)-2=0 rArr t^(2)=2 rArr t=pmsqrt2` `therefore" lines are "x= pm sqrt2(y-2)`
