Questions

Solution

(1) Find the slope of the straight line

(i) 3x + 4 y – 6 = 0

(ii) y = 7 x + 6

(iii) 4x = 5 y + 3

Solution

(2) Show that the straight lines x + 2 y + 1 = 0 and 3 x + 6 y + 2 = 0 are parallel.

Solution

(3) Show that the straight lines 3 x – 5 y + 7 = 0 and 15 x + 9 y + 4 = 0 are perpendicular

Solution

(4) If the straight lines y/2= x – p and x + 5 = 3 y are parallel, then find a

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(5) Find the value of a if the straight lines 5 x – 2 y – 9 = 0 and ay + 2 x – 11 = 0 are perpendicular to each other.

Solution

(6) Find the value of p for which the straight lines 8 px + (2-3p) y + 1 = 0 and px + 8 y – 7 =0 are perpendicular to each other.

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(7) If the straight line passing through the points (h,3) and (4,1) intersects the line 7 x – 9 y – 19 = 0 t a right angle, find the value of h.

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(8) Find the equation of the straight line parallel to the line 3x – y + 7 =0 and passing through the point (1,-2)

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(9) Find the equation of the straight line perpendicular to the straight line x – 2 y + 3 = 0 and passing through the point (1,-2).

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(10) Find the equation of the perpendicular bisector of the straight line segment joining the points (3, 4) and (-1, 2).

Solution

(11) Find the equation of the straight line passing through point of intersection of the lines 2 x + y – 3 =0 and 5 x + y – 6 = 0 and parallel to the lie joining the points (1,2) and (2,1)

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(12) Find the equation of the straight line passing through the point of intersection of the 5x – 6 y = 1 and 3x + 2y + 5 = 0 and is perpendicular to the straight line 3x – 5 y + 11 = 0.

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(13) Find the equation of the straight line joining the point of intersection of the lines 3 x – y + 9 = 0 ad x + 2 y = 4 and the point of intersection of the lines 2 x + y – 4 = 0 and x – 2 y + 3 = 0.

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(14) If the vertices of a triangle ABC are A (2,-4), B (3,3) and C (-1,5). Find the equation of the straight line along the altitude from vertex B.

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(15) If the vertices of triangle ABC are (-4, 4) , B (8 ,4) and C (8,10). Find the equation of the straight line along the median from A.

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(16) Find the coordinates of the foot from the origin on the straight line 3 x +2 y = 13.

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(17) If x + 2 y = 7 and 2 x + y = 8 are the equations of the lines of two diameter of the circle, find the radius of the circle if the point (0,-2) lie on the circle.

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(18) Find the equation of the straight line segment whose end points are the point of intersection of the straight lines 2 x – 3 y + 4  = 0, x – 2 y + 3 = 0 and the midpoint of the line joining the points (3 ,-2) and (-5 , 8).

Solution

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(19) If the isosceles triangle PQR, PQ = PR. The base QR lies on the axis, P lies on the y-axis and 2 x – 3 y + 9 =0 is the equation of PQ. Find the equation of PQ. Find the equation of the straight line along PR.

Solution