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In the xy-plane, how many straight lines...

In the xy-plane, how many straight lines whose x-intercept is a prime number and whose y-intercept is a positive integer pass through the point (4,3)?

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
The line `(x)/(p) +(y)/(q) =1`, where 'p' is a prime and 'q' is a positive integer, passes through (4,3).
`:. (4)/(p) +(3)/(q) =1`
`:. q = (3p)/(p-4) =3+(12)/(p-4)`
Since, q is a positie integer, `p gt 4` and `(p-4)` divides 12, there are only two such prime numbers,
`p = 5` and `p = 7`
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Knowledge Check

  • In a plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point , on line passes through both points A and B , and no two are parallel. Them the number of interaction points the lines have is equal to

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    D
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    B
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    C
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    D
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