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

Question

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

Tardigrade Admin · Accepted Answer

Both statements are true and statement-2 is the correct explanation of statement-1

∴

The straight line

y = m x + \frac{a}{m}

is always a tangent to the parabola

y^{2} = 4 a x

for any value of

m

.
The co-ordinates of point of contact

(\frac{a}{m ^{2}}, \frac{2 a}{m})

Q. Statement-1: The line x−2y=2 meets the parabola, y2+2x=0 only at the point (−2,−2). Statement-1: The line y=mx−2m1​(m=0) is tangent to the parabola, y2=−2x at the point (−2m21​,−m1​).

Statement-1 is true; Statement-2 is false

Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1

Statement-1 is false; Statement-2 is true

Statement-1 a true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1

Both statements are true and statement-2 is the correct explanation of statement-1 ∴ The straight line y=mx+ma​ is always a tangent to the parabola y2=4ax for any value of m. The co-ordinates of point of contact (m2a​,m2a​)

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

Both statements are true and statement-2 is the correct explanation of statement-1
$∴$ The straight line $y = m x + \frac{a}{m}$ is always a tangent to the parabola $y^{2} = 4 a x$ for any value of $m$ .
The co-ordinates of point of contact $(\frac{a}{m ^{2}}, \frac{2 a}{m})$