If the parabola y2 = 4ax passes through the point (1, -2), then the tangent at this point is

Question

If the parabola y2 = 4ax passes through the point (1, -2), then the tangent at this point is (A) x + y- 1 = 0 (B) x-y-1 = 0 (C) x + y + 1 = 0 (D) x-y- 1=0

Tardigrade Admin · Accepted Answer

Since the parabola y2 = 4ax passes through the point (1, -2), ∴ (-2)2 = 4a(I) ⇒ a = 1 Equation of tangent to the parabola at (1,-2) yy1 =2a(x + x1) or y(-2) = 2(1)(x+1) or x + y+1 = 0

Q. If the parabola $y^{2} = 4 a x$ passes through the point $(1, - 2)$ , then the tangent at this point is

$x + y - 1 = 0$

$x - y - 1 = 0$

$x + y + 1 = 0$

$x - y - 1 = 0$

Since the parabola $y^{2} = 4 a x$ passes through the point $(1, - 2)$ ,
$∴ (- 2)^{2} = 4 a (I) \Rightarrow a = 1$
Equation of tangent to the parabola at $(1, - 2)$
$y y_{1} = 2 a (x + x_{1})$ or
$y (- 2) = 2 (1) (x + 1)$ or $x + y + 1 = 0$

Q. If the parabola y2=4ax passes through the point (1,−2), then the tangent at this point is

x+y−1=0

x−y−1=0

x+y+1=0

x−y−1=0

Since the parabola y2=4ax passes through the point (1,−2), ∴(−2)2=4a(I)⇒a=1 Equation of tangent to the parabola at (1,−2) yy1​=2a(x+x1​) or y(−2)=2(1)(x+1) or x+y+1=0

Q. If the parabola $y^{2} = 4 a x$ passes through the point $(1, - 2)$ , then the tangent at this point is

$x + y - 1 = 0$

$x - y - 1 = 0$

$x + y + 1 = 0$

$x - y - 1 = 0$

Since the parabola $y^{2} = 4 a x$ passes through the point $(1, - 2)$ ,
$∴ (- 2)^{2} = 4 a (I) \Rightarrow a = 1$
Equation of tangent to the parabola at $(1, - 2)$
$y y_{1} = 2 a (x + x_{1})$ or
$y (- 2) = 2 (1) (x + 1)$ or $x + y + 1 = 0$