PAIR OF STRAIGHT LINES PROBLEMS WITH SOLUTION

About "Pair of Straight Lines Problems With Solution"

Pair of Straight Lines Problems With Solution :

Here we are going to see some practice questions on pair of straight lines.

Pair of Straight Lines Problems With Solution - Practice questions

(1) Find the combined equation of the straight lines whose separate equations are x − 2y −3 = 0 and x + y+5 = 0. Solution

(2) Show that 4x² + 4xy + y² − 6x − 3y − 4 = 0 represents a pair of parallel lines. Solution

(3) Show that 2x² + 3xy − 2y² + 3x + y + 1 = 0 represents a pair of perpendicular lines. Solution

(4) Show that the equation 2x² −xy−3y² −6x + 19y − 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is tan⁻¹(5). Solution

(5) Prove that the equation to the straight lines through the origin, each of which makes an angle α with the straight line y = x is x² − 2xy sec 2α + y² = 0 Solution

(6) Find the equation of the pair of straight lines passing through the point (1, 3) and perpendicular to the lines 2x − 3y+1 = 0 and 5x + y − 3 = 0 Solution

(7) Find the separate equation of the following pair of straight lines

(i) 3x² + 2xy − y² = 0 Solution

(ii) 6(x − 1)² + 5(x − 1)(y − 2) − 4(y − 2)² = 0 Solution

(iii) 2x² − xy − 3y² − 6x + 19y − 20 = 0 Solution

(8) The slope of one of the straight lines ax² + 2hxy + by² = 0 is twice that of the other, show that 8h² = 9ab. Solution

(9) The slope of one of the straight lines ax² + 2hxy + by² = 0 is three times the other, show that 3h² = 4ab. Solution

(10) A ΔOPQ is formed by the pair of straight lines x² −4xy +y²= 0 and the line PQ. The equation of PQ is x + y − 2 = 0. Find the equation of the median of the triangle ΔOPQ drawn from the origin O. Solution

(11) Find p and q, if the following equation represents a pair of perpendicular lines

6x² + 5xy − py² + 7x + qy − 5 = 0 Solution

(12) Find the value of k, if the following equation represents a pair of straight lines. Further, find whether these lines are parallel or intersecting, 12x² + 7xy − 12y² − x + 7y + k = 0 Solution

(13) For what value of k does the equation 12x²+2kxy+2y²+11x−5y+2 = 0 represent two straight lines.

Solution

(14) Show that the equation 9x²− 24xy + 16y²− 12x + 16y − 12 = 0 represents a pair of parallel lines. Find the distance between them. Solution

(15) Show that the equation 4x² + 4xy + y² − 6x − 3y −4 = 0 represents a pair of parallel lines. Find the distance between them. Solution

(16) Prove that one of the straight lines given by ax² + 2hxy + by² = 0 will bisect the angle between the co-ordinate axes if (a + b)² = 4h²Solution

(17) If the pair of straight lines x² − 2kxy − y² = 0 bisect the angle between the pair of straight lines x² − 2lxy − y² = 0, Show that the later pair also bisects the angle between the former. Solution

(18) Prove that the straight lines joining the origin to the points of intersection of 3x² + 5xy − 3y² + 2x + 3y = 0 and 3x − 2y − 1 = 0 are at right angles. Solution

PAIR OF STRAIGHT LINES PROBLEMS WITH SOLUTION

About "Pair of Straight Lines Problems With Solution"

Pair of Straight Lines Problems With Solution - Practice questions

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