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The number of lines that are parallel to 2x + 6y- 7= 0 and have an intercept 10 between the coordinate axes is : - (a) 1 (b) 2 (c) 4 (d) infintely many
y = mx + c................1 2x + 6y - 7 = 0 m = -1/3 so the eq of line which is parallel to above line is y = -x/3 + c ................2 y intercept = (0,c) x intercept = (3c,0) y using distance formula , distance bw these two points will be d = (9c2 + c2)1/2 = (+ or - )(root10)c (distance bw coordinate axis) d = 10 (given) so c = + or - (root10) there are two possible values for c so total number of lines can be 2 ...
y = mx + c................1
2x + 6y - 7 = 0
m = -1/3 so the eq of line which is parallel to above line is
y = -x/3 + c ................2
y intercept = (0,c)
x intercept = (3c,0)
y using distance formula , distance bw these two points will be
d = (9c2 + c2)1/2 = (+ or - )(root10)c (distance bw coordinate axis)
d = 10 (given) so
c = + or - (root10)
there are two possible values for c so total number of lines can be 2 ...
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