Question

1) For what value of k does
12x2 + 7xy + ky2 + 13x - y + 3 = 0 represents
a pair of straight lines?​

Answer 1

$\huge \mathscr{\orange {\underline{\pink{\underline {Answer:-}}}}}$

Comparing the given equation with the second degree general equation,

we have ,

a = 12,

h = 7/2,

b = k,g = 13/2,

f = -1/2 and

c = 3

Since the equation represents pair of lines,

we get,

△ = abc + 2fgh - af² - bg² - ch² = 0

That is,

(12)(k)(3)+2(-1/2)(13/2)(7/2)-12(¼)-k(169/4)-3(49/4) = 0

=> 144k - 91 - 12 - 169k - 147 = 0

=> -25k = 250

=> k = -10.

Answer 2

Comparing the given equation with the seconddegree general equation,
we have a = 12,h = 7/2, b = k,g = 13/2, f = -1/2 and c = 3
Since the equation represents pair of lines, we get