How many lines can pass through two given points?

Geometry Level pending

If the circles $x^{2}+y^{2}+2ax+cy+a=0$ and $x^{2}+y^{2}-3ax+dy-1=0$ intersect in two distinct points $P$ and $Q$ , then the line $5x+by-a=0$ passes through $P$ and $Q$ for $\text{\_\_\_\_\_\_\_\_\_\_}$ .

Infinitely many values of

a

No value of

a

Exactly one value of

a

Exactly two values of

a

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How many lines can pass through two given points?

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