Question

The values of h for which the equation
3x2 + 2hxy – 3y2 – 40x + 30y - 75 = 0 represents a pair
of straight lines, are
(a) 4,4
(b) 4,6
(c) 4,4
(d) 0,4

Answer 1

We get repeated values of h as 2,2.

Step-by-step explanation:

Since we know that;

• The equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of straight lines  

When, $abc+2fgh-af^2-bg^2-ch^2=0$  ......(1)

• So, we are given the equation:

   $3x^2 + 2hxy - 3y^2- 40x + 30y -75=0$

By comparing this equation with the standard equation, we get as;

a = 3, b = -3, c = -75, f = 15, g = -20, h = h

Put these values of variable in equation (i), we get.

• $3\times(-3)\times(-75)+2(15)\times(-20) \times h-3 (15)2+3 (-20)2+75h^2=0$

On further simplification, we get,

• $675-600h-675+1200+75h^2=0$

$75h^2-600h+1200=0$

$h^2-8h+16=0$

$(h-4)^2=0$

h=4,4

Thus, we get repeated values of h as 2.

Answer 2

Answer:

We get repeated values of h as 2,2.

Step-by-step explanation:

Since we know that;

The equation  represents a pair of straight lines  

When,   ......(1)

So, we are given the equation:

   

By comparing this equation with the standard equation, we get as;

a = 3, b = -3, c = -75, f = 15, g = -20, h = h

Put these values of variable in equation (i), we get.

On further simplification, we get,

h=4,4

Thus, we get repeated values of h as 2.