If the line $m (x - 1) - m^{2} (y - 1) + 1 = 0$ is a tangent to a parabola for any real value of m, then the equation of the parabola is

x^{2} + 2 x + 4 y + 3 = 0

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(y - 1)^{2} = 4 (x - 1)

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(y - 1)^{2} = - 4 (x - 1)

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x^{2} - 2 x + 4 y - 3 = 0

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Solution

The correct option is D $x^{2} - 2 x + 4 y - 3 = 0$
$(x - 1) = m (y - 1) - \frac{1}{m}$
The parabola is $(x - 1)^{2} = - 4 (y - 1)$

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If the line m(x−1)−m2(y−1)+1=0 is a tangent to a parabola for any real value of m, then the equation of the parabola is

The correct option is D x2−2x+4y−3=0(x−1)=m(y−1)−1m The parabola is (x−1)2=−4(y−1)

If the line $m (x - 1) - m^{2} (y - 1) + 1 = 0$ is a tangent to a parabola for any real value of m, then the equation of the parabola is

The correct option is D $x^{2} - 2 x + 4 y - 3 = 0$
$(x - 1) = m (y - 1) - \frac{1}{m}$
The parabola is $(x - 1)^{2} = - 4 (y - 1)$