The equations of the sides of a square whose each side is of length 4 units and centre is (1, 1) Given that one pair of sides is parallel to 3x - 4y = 0
A
3x−4y+11=0,3x−4y−9=0,4x+3y+3=0,4x+3y−17=0
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B
3x−4y−15=0,3x−4y+5=0,4x+3y+3=0,4x+3y−17=0
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C
3x−4y+11=0,3x−4y−9=0,4x+3y+2=0,4x+3y−18=0
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D
None
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Solution
The correct option is A3x−4y+11=0,3x−4y−9=0,4x+3y+3=0,4x+3y−17=0
Given the centre of square is A(1,1) and length of square is 4
one side of square is parallel to line 3x−4y=0 hence
The equation of one side is3x−4y+λ=0
The perpendicular distance from centre of square to all sides is 2
Hence ∣∣
∣∣3−4+λ√32+42∣∣
∣∣=2
−1+λ√25=±2
−1+λ=±10
λ=11 and λ=−9
Hence Eq of sides 3x−4y+11=0 and 3x−4y−9=0
Now the other two sides of square should be perpendicular
Hence equation of sides is 4x+3y+μ=0
The perpendicular distance from centre of square to all sides is 2
Hence ∣∣
∣∣4+3+μ√32+42∣∣
∣∣=2
7+μ√25=±2
7+μ=±10
μ=3 and μ=−17
Hence Eq of other two sides 4x+3y+3=0 and 4x+3y−17=0