Equation of the tangent to the hyperbola 2x2-3y2=6 . Which is parallel to the line y-3x-4=0 is

Question

Equation of the tangent to the hyperbola 2x2-3y2=6 . Which is parallel to the line y-3x-4=0 is (A)  y=3x+8  (B)  y=3x-8  (C)  y=3x+2  (D) None of these

Tardigrade Admin · Accepted Answer

Let the equation of a line which is parallel to the line

y - 3 x - 4 = 0

is

y = 3 x + k

Since, this is tangent to the hyperbola

\frac{x ^{2}}{3} - \frac{y ^{2}}{2} = 1

∴

k = 3 (3)^{2} - 2

(∵ k = a^{2} m^{2} - b^{2})

= 25 = 5

∴

Required line is

y = 3 x + 5

,

Q. Equation of the tangent to the hyperbola $2 x^{2} - 3 y^{2} = 6$ . Which is parallel to the line $y - 3 x - 4 = 0$ is

$y = 3 x + 8$

$y = 3 x - 8$

$y = 3 x + 2$

None of these

Let the equation of a line which is parallel to the line
$y - 3 x - 4 = 0$ is $y = 3 x + k$
Since, this is tangent to the hyperbola
$\frac{x ^{2}}{3} - \frac{y ^{2}}{2} = 1$
$∴$ $k = 3 (3)^{2} - 2$
$(∵ k = a^{2} m^{2} - b^{2})$
$= 25 = 5$
$∴$ Required line is $y = 3 x + 5$ ,

Q. Equation of the tangent to the hyperbola 2x2−3y2=6 . Which is parallel to the line y−3x−4=0 is

y=3x+8

y=3x−8

y=3x+2