Question

If the line 2x - y = 4 touches the hyperbola
4x^2 - 3y^2 = 24, the point of contact is​

Answer 1

The point of contact will be (3,2).

Step-by-step explanation:

The point of line touching of hyperbola will be the point that will satisfy both the equations,

Equation of line : $2x-y=4$..[1]

Equation of hyperbola given :

$4x^2-3y^2=24$

Putting value of y from [1] in [2]:

y = 2x-4

$4x^2-3(2x-4)^2=24$

$4x^2-3(4x^2+16-16x)=24$

$4x^2-12x^2-48+48x=24$

$-8x^2+48x=24+48$

$8x^2-48x+72=0$

$x^2-6x+9=0$

$x^2-3x-3x+9=0$

$x(x-3)-3(x-3)=0$

(x-3)(x-3)=0

x = 3

y = 2x - 4 = 2 × 3 - 4 = 2

The point of contact will be (3,2).

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