Answer to Question #278870 in Analytic Geometry for Biniyam

Question #278870

Determine the value of a and b for which the two lines ax - 2y = 0 and 6x - 4y = b 1have exactly one intersection point 2 are distnict parallel lines 3 concide 4 perpendicular to eachother

1
Expert's answer
2021-12-13T15:23:48-0500
"ax-2y=2=>y=\\dfrac{a}{2}x-1"

"6x-4y=b=>y=\\dfrac{3}{2}x-\\dfrac{b}{4}"

1.


"\\dfrac{a}{2}\\not=\\dfrac{3}{2}=>a\\not=3, b\\in \\R"

2.


"\\begin{matrix}\n \\dfrac{a}{2}=\\dfrac{3}{2} \\\\\n -1\\not=-\\dfrac{b}{4}\n\\end{matrix}=>a=3, b\\not=4"

3.


"a=3, b=4"

4.

"\\dfrac{a}{2}\\cdot\\dfrac{3}{2}=-1=>a=-\\dfrac{4}{3}, b\\in \\R"


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