Statement-1: The line x-2 y=2 meets the parabola y2+2 x=0 only at one point (-2,-2). Statement-2: The line y=m x-(1/2 m)(m ≠ 0) is tangent to the parabola y2=-2 x at the point ((-1/2 m2), (-1/m)).

Question

Statement-1: The line x-2 y=2 meets the parabola y2+2 x=0 only at one point (-2,-2). Statement-2: The line y=m x-(1/2 m)(m ≠ 0) is tangent to the parabola y2=-2 x at the point ((-1/2 m2), (-1/m)). (A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (C) Statement-1 is true, statement-2 is false. (D) Statement-1 is false, statement-2 is tru

Tardigrade Admin · Accepted Answer

The line of slope =m given by y=m x+c is tangent to parabola y2=4 a x, if c=(a/m) and the point of contact is (( a / m 2), (2 a / m )). Here, m =(1/2), c =-1 and a =(-1/2)

Q. Statement-1: The line $x - 2 y = 2$ meets the parabola $y^{2} + 2 x = 0$ only at one point $(- 2, - 2)$ .
Statement-2: The line $y = m x - \frac{1}{2 m} (m \neq = 0)$ is tangent to the parabola $y^{2} = - 2 x$ at the point $(\frac{- 1}{2 m ^{2}}, \frac{- 1}{m})$ .

Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is true, statement-2 is false.

Statement-1 is false, statement-2 is tru

The line of slope $= m$ given by $y = m x + c$ is tangent to parabola $y^{2} = 4 a x$ , if $c = \frac{a}{m}$ and the point of contact is $(\frac{a}{m ^{2}}, \frac{2 a}{m})$ .
Here, $m = \frac{1}{2}, c = - 1$ and $a = \frac{- 1}{2}$

Q. Statement-1: The line x−2y=2 meets the parabola y2+2x=0 only at one point (−2,−2). Statement-2: The line y=mx−2m1​(m=0) is tangent to the parabola y2=−2x at the point (2m2−1​,m−1​).