Q38 / 90 · JEE Main 2019 (12 Apr Shift 2) · Mathematics

The equation of a common tangent to the curves, $y^{2} = 16 x$ and $x y = - 4,$ is:

A
$x - 2 y + 16 = 0$
Correct answer
B
$x - y + 4 = 0$
C
$2 x - y + 2 = 0$
D
$x + y + 4 = 0$

Solution

A tangent to the parabola $y^{2} = 16 x$ can be written as:
$y = m x + \frac{4}{m}$ …. (1)
It will touch the hyperbola $x y = - 4,$ if the quadratic $x (m x + \frac{4}{m}) = - 4$ has coincident roots,
$\Rightarrow (m^{2}) x^{2} + 4 x + 4 m = 0, D \equiv 16 - 16 m^{3} = 0$
$\Rightarrow m = 1$
$\Rightarrow$ Equating of common tangent will be $y = x + 4$
$\Rightarrow x - y + 4 = 0$

Hence, the correct answer is option: 'B'.

More Hyperbola Questions

For the hyperbola H : x 2 - y 2 = 1 and the ellipse E : x 2 a 2 + y 2 b 2 = 1 , a b 0 , let the (1) eccentricity of E be reciprocal of the e28 Jul, 2022 (M)Common Tangent
A common tangent T to the curves C 1 : x 2 4 + y 2 9 = 1 and C 2 : x 2 42 - y 2 143 = 1 does not pass through the fourth quadrant. If T touc27 Jul, 2022 (E)Common Tangent
Let a line L : 2 x + y = k , k 0 be a tangent to the hyperbola x 2 - y 2 = 3 . If L is also a tangent to the parabola y 2 = x , then is equa22 Jul, 2021 (M)Common Tangent
If the line y = m x + c is a common tangent to the hyperbola x 2 100 - y 2 64 = 1 and the circle x 2 + y 2 = 36 , then which one of the foll05 Sep, 2020 (E)Common Tangent
Equation of a common tangent to the parabola and the hyperbola is :11 Jan, 2019 (M)Common Tangent
If the eccentricity of the hyperbola , passing through , satisfies , then the length of the latus rectum of the hyperbola is:06 Apr, 2026 (M)Equation of hyperbola

The equation of a common tangent to the curves, y2=16x and xy=-4, is:

Solution

More Hyperbola Questions

The equation of a common tangent to the curves, $y^{2} = 16 x$ and $x y = - 4,$ is: