Answer to Question #278867 in Analytic Geometry for Biniyam

Question

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

Answer 1

$$ax-2y=2=>y=\dfrac{a}{2}x-1$$

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

1.

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

2.

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

3.

$$a=3, b=4$$

4.

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