Home
Class 12
MATHS
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`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    CENGAGE|Exercise Comprehension Type|3 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • STATISTICS

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

Similar Questions

Explore conceptually related problems

How many lines pass through point (2,3) such that its x -intercept is a prime no.and y- intercept is a positive integer?

Find the equation of a line , whose y-intercept is -5 and passes through point A (-3,2) .

The equation of straight line whose inclination is (pi)/(4) and x -intercept is 4

find the gradient and intercepts on the axes of the straight line passing through the point (1,-3) and (4,5)

Find the equation of the straight line whose intercepts on the axes are twice the intercepts of the straight line 3x+4y=6 .

A straight line cuts intercepts from the coordinate axes sum of whose reciprocals is (1)/(p). It passses through a fixed point

Lines whose combined equation is xy+3x-2y-6=0 pass through the point

Equation of the straight line making equal intercepts on the axes and passing through the point (2,4) is