PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to the line x − 2y = 1.

Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x − 4y+ 8 = 0.

Find the distance of the line 2x + y = 3 from the point (−1, −3) in the direction of the line whose slope is 1.

The perpendicular distance of a line from the origin is 5 units and its slope is − 1. Find the equation of the line.

Find the equation of a line perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and at a distance of 3 units from the origin.

Find the distance of the point (4, 5) from the straight line 3x − 5y + 7 = 0.

Find the perpendicular distance of the line joining the points (cos θ, sin θ) and (cos ϕ, sin ϕ) from the origin.

Show that the perpendiculars let fall from any point on the straight line 2x + 11y − 5 = 0 upon the two straight lines 24x + 7y = 20 and 4x − 3y − 2 = 0 are equal to each other.

Find the distance of the point of intersection of the lines 2x + 3y = 21 and 3x − 4y + 11 = 0 from the line 8x + 6y + 5 = 0.

What are the points on X-axis whose perpendicular distance from the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] is a ?

Show that the product of perpendiculars on the line \[\frac{x}{a} \cos \theta + \frac{y}{b} \sin \theta = 1\]  from the points \[( \pm \sqrt{a^2 - b^2}, 0) \text { is }b^2 .\]

Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line \[x - \sqrt{3}y + 4 = 0 .\]

What are the points on y-axis whose distance from the line \[\frac{x}{3} + \frac{y}{4} = 1\]  is 4 units?

Show that the path of a moving point such that its distances from two lines 3x − 2y = 5 and 3x + 2y = 5 are equal is a straight line.

If sum of perpendicular distances of a variable point P (x, y) from the lines x + y − 5 = 0 and 3x − 2y + 7 = 0 is always 10. Show that P must move on a line.

If the length of the perpendicular from the point (1, 1) to the line ax − by + c = 0 be unity, show that \[\frac{1}{c} + \frac{1}{a} - \frac{1}{b} = \frac{c}{2ab}\] .

Determine the distance between the pair of parallel lines:

4x − 3y − 9 = 0 and 4x − 3y − 24 = 0

Determine the distance between the pair of parallel lines:

8x + 15y − 34 = 0 and 8x + 15y + 31 = 0

Determine the distance between the pair of parallel lines:

y = mx + c and y = mx + d

Determine the distance between the pair of parallel lines:

4x + 3y − 11 = 0 and 8x + 6y = 15