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Question

If pis the length of the perpendicular from the origin to the line, whose intercepts with the coordinate axes are 13 and 14 then the value of p is


A

35

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B

112

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C

15

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D

5

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Solution

The correct option is C

15


Explanation for the correct options:

Step 1: Apply coordinate identities

The intercepts with the coordinate axes are 13 and 14.

So, the line passes through 13,0 and 0,14

The slope of the line = 14-00-13=-34 and the y-intercept is 14
Step 2: Put this value in the below equation

The equation of the line is : (y-y1)=m(x-x1)

y-0=-34x-13

∴y=-34x+14

Simplifying this equation we get,

∴3x+4y=1

Step 3: The length of the perpendicular from the origin,

p=±ax1+by1+ca2+b2, where p is the length and a=3,b=4,x1=0,y1=0,andc=1

∴P=3×0-4×0+132+42=19+16=125=15

Hence option (3) is correct.


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