If the lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other, find the relation connecting a and b.

Given, Lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other. Then the product of their slopes is -1. Converting 3x + by + 5 = 0 in the form y = mx + c. ⇒ by = -3x - 5 ⇒ y = . Comparing with y = mx + c we get, Slope of first line = m 1 = . Converting ax - 5y + 7 = 0 in the form y = mx + c. ⇒ 5y = ax + 7 ⇒ y = . Comparing with y = mx + c we get, Slope of second line = m 2 = . For perpendicular lines, product of their slopes is -1. ∴ m 1 .m 2 = -1. Hence, the relation between a and b is given by 3a = 5b.

Lines 2x - by + 5 = 0 and ax + 3y = 2 are parallel. Find the relation connecting a and b.

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If the straight lines 3x - 5y + 7 = 0 and 4x + ay + 9 = 0 are perpendicular to one another, find the value of a.

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Is the line through (-2, 3) and (4, 1) perpendicular to the line 3x = y + 1? Does the line 3x = y + 1 bisect the join of (-2, 3) and (4, 1)?

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The line through A(-2, 3) and B(4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.

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Mathematics

If the lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other, find the relation connecting a and b.

Straight Line Eq

Related Questions

Lines 2x - by + 5 = 0 and ax + 3y = 2 are parallel. Find the relation connecting a and b.

If the straight lines 3x - 5y + 7 = 0 and 4x + ay + 9 = 0 are perpendicular to one another, find the value of a.

Is the line through (-2, 3) and (4, 1) perpendicular to the line 3x = y + 1? Does the line 3x = y + 1 bisect the join of (-2, 3) and (4, 1)?

The line through A(-2, 3) and B(4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.