CAT Exam Model Paper 5 with solutions for free online practice

Question : 2 of 60

Marks: +1, -0

In the X-Y plane two distinct lines are drawn parallel to the line 3y - 4x = 15, each at a distance of 3 units from the given straight line. What are the lengths of the line segments of these two lines lying inside the circle

x^{2}

+ y

^{2}

= 25?

6 and 8
0 and 8
0 and 10
8 and 10

Validate

Solution:

Distance of origin (0,0) from the line 3y- 4x -1 5 = 0:

| { 3 ( 0 ) - 4 ( 0 ) - 15 }/ {√ { 3 ^ { 2 } + 4 ^ { 2 } } } | = { 15 }/ { 5 } = 3

units
Let the new lines drawn parallel to 3y - 4x - 15 = 0 be L

_1

and L

_{2}

.
Distance of L

_1

from origin = 3 + 3 = 6 units
Distance of L

_{2}

from origin = 3 - 3 = 0 units
The circle x

^{2}

+ y

^{2}

= 25 has a radius of 5 units.
Hence line segment of L

_1

lying inside the circle will be of zero length (L

_1

does not cut the circle).
Chord cut by L

_{2}

will be diameter = 10 units

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