If the straight line y=m x+c touches the parabola y²-4 a x+4 a³=0, then c is

Correct Answer is : am−a2m\;a/m-a² mma−a2m

Correct Answer is : am−a2m\;a/m-a² mma−a2m

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BITSAT 2022 Paper

Section: Mathematics

Question : 103 of 130

Marks: +1, -0

If the straight line

y=m x+c

y^2-4 a x+4 a^3=0

c

Solution: 👈: Video Solution

Solving the given equations,

(mx +c)^2 = 4ax - a^3

\Rightarrow m^2x^2 + 2mc \cdot x + c^2 = m4ax - 4a^3

\Rightarrow m^2x^2 +(2mc - 4a) x+c^2 + 4a^3 =0

Since the straight line touches the parabola at a point,

so, the discriminant

=0

\Rightarrow (2mc - 4a)^2 -4m^2 (c^2+4a^3)=0

\Rightarrow 4m^2c^2 - 16amc +16a^2 - 4m^2c^2-16 a^3m^2=0

\Rightarrow -mc +a-a^2m^2=0

\Rightarrow mc =a-a^2m^2 \Rightarrow c=\frac{a}{m} - a^2m

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