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Question: Condition on 'a' and 'b', such that a point can be found so that two tangents can be drawn from it t...

Condition on 'a' and 'b', such that a point can be found so that two tangents can be drawn from it to parabola S1 = 0 are normals to the parabola S2= 0 is-

A

a2> 4b2

B

a2> 8b2

C

a2< 8b2

D

None

Answer

a2> 8b2

Explanation

Solution

Equation of tangent of S1 = 0 is

y = mx +... (1)

& equation of normal s2 = 0

y = mx + 2b +... (2)

If both (1) and (2) are same then

11\frac { 1 } { 1 } = mm\frac { \mathrm { m } } { \mathrm { m } }= Ž 2b +=

Ž 2bm2 + b = am

Ž 2bm2 –am + b = 0

Q m is to be real

so D > 0 Ž a2 – 8b2 > 0

a2 > 8b2