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If x²/a + y²/b + 2xy/h = 0 represents a pair of straight lines and slope of one line is twice the other, then ab : h² is

1) 9 : 8 2) 8 : 9 3) 1 : 2 4) 2 : 1 Solution: Given x2/a +... View Article

If one of the lines represented by the equation ax² + 2hxy + by² = 0 be y = mx, then

1) bm2 + 2hm + a = 0 2) bm2 + 2hm – a = 0 3) am2 + 2hm... View Article

A general equation of second degree ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents a pair of straight lines if

1) h2 = 2ab 2) h2 > 2ab 3) \(\begin{array}{l}\begin{vmatrix} a &h &g \\ h & b& f\\ g& f... View Article

Which of the following second degree equation represents a pair of straight lines?

1) x2 – xy – y2 = 1 2) –x2 + xy – y2 = 1 3) 4x2 – 4xy... View Article

The equation of the perpendiculars drawn from the origin to the lines represented by the equation 2x² – 10xy + 12y² + 5x – 16y – 3 = 0 is

1) 6x2 + 5xy + y2 = 0 2) 6y2+ 5xy + x2 = 0 3) 6x2 – 5xy +... View Article

The nature of straight lines represented by the equation 4x² + 12xy + 9y² = 0, is

1) Real and coincident 2) Real and different 3) Imaginary and different 4) None of the above Solution: Given 4x2... View Article

The equation of the lines represented by the equation ab(x² – y²) + (a² – b²)xy = 0 are

1) ax – by = 0, bx + ay = 0 2) ax – by = 0, bx – ay... View Article

Separate equations of lines, for a pair of lines, whose equation is x² + xy – 12y² = 0 are

1) x + 4y = 0 and x + 3y = 0 2) 2x – 3y = 0 and x... View Article

If the equation ax² + 2hxy + by² = 0 has the one line as the bisector of angle between the coordinates axes, then

1) (a – b)2 = h2 2) (a + b)2 = h2 3) (a – b)2 = 4h2 4) (a... View Article

If r(1 – m²) + m(p – q) = 0, then a bisector of the angle between the lines represented by the equation px² – 2rxy + qy² = 0, is

1) y = x 2) y = –x 3) y = mx 4) my = x Solution: Given equation of... View Article

If the bisectors of the angles between the pairs of lines given by the equation ax² + 2hxy + by² = 0 and ax² + 2hxy + by² + λ(x² + y²) = 0 be coincident, then λ =

1) a 2) b 3) h 4) Any real number Solution: Given angle bisectors are coincident. This means the angle... View Article

If y = mx be one of the bisectors of the angle between the lines ax² – 2hxy + by² = 0 ,then

1) h(1 + m2) + m (a – b) = 0 2) h(1 – m2) + m (a + b)... View Article

The equation of the bisectors of the angle between lines represented by equation 4x² – 16xy – 7y²= 0 is

1) 8x2 + 11xy – 8y2 = 0 2) 8x2 – 11xy – 8y2 = 0 3) 16x2 + 11xy... View Article

The pair of straight lines joining the origin to the points of intersection of the line y = 2√2 x + c and the circle x² + y² = 2 are at right angles, if

1) c2 – 4 = 0 2) c2 – 8 = 0 3) c2 – 9 = 0 4) c2... View Article

Two lines are given by (x – 2y)² + k(x – 2y) = 0. The value of k so that the distance between them is 3, is

1) 1/√3 2) 2/5 3) ±3√5 4) None of these Solution: Given (x – 2y)2 + k(x – 2y) =... View Article

If the distance of a point (x₁,y₁) from each of the two straight lines, which pass through the origin of coordinates, is d, then the two lines are given by

1) (xy1 – yx1)2 = d2(x2 + y2) 2) (x1y1 – xy)2 = (x2 + y2) 3) (xy1 + x1y)2... View Article

The equation of pair of straight lines joining the point of intersection of the curve x² + y² = 4 and y – x = 2 to the origin, is

1) x2 + y2 = (y – x)2 2) x2 + y2 + (y – x)2 = 0 3) x2... View Article

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve x² + y² = 4 with x + y = a. The set containing the value of a is

1) {–2, 2} 2) {–3, 3} 3) {–4, 4} 4) {–5, 5} Solution: Given curve is x2 + y2 =... View Article

The equation of the line joining origin to the points of intersection of the curve x² + y² = a² and x² + y² – ax – ay = 0 is

1) x2 – y2 = 0 2) xy = 0 3) xy – x2 = 0 4) y2 + xy... View Article

Distance between two lines represented by the pair of straight lines x² – 6xy + 9y² + 3x – 9y – 4 = 0 is

1) 1/2 2) 5/√2 3) √10 4) √(5/2) Solution: Given x2 – 6xy + 9y2 + 3x – 9y –... View Article

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