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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 = (x2 - y2) 4) (x2 - y2) = 2(x1 + y1) Solution: The equation of a... 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 + y2 = 4(y - x)2 4) x2 + y2 + 4(y - x)2 = 0 Solution: Given curve is x2 + y2 = 4 ..(i)... 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 = 4 ..(i) This is a circle with radius = 2 and centre (0, 0).... 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 = 0 Solution: Given x2 + y2 = a2 ..(i) x2 + y2 - ax - ay = 0 => x2 + y2 = a(x +... 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 - 4 = 0 Comparing with ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 We get... View Article

The graph of y = |x| consists of a pair of straight lines lying

1) To the left of y-axis 2) Above x-axis 3) Below x-axis 4) To the right of y-axis Solution: Given y = |x| When x is positive, the value of... View Article

The area enclosed by the pair of lines xy = 0, the line x – 4 = 0 and y + 5 = 0 is

1) 20 sq.units 2) 10 sq.units 3) 5/4 sq.units 4) 0 sq.units Solution: Given xy = 0 => x = 0 and y = 0 x - 4 = 0 y + 5 = 0 The graph is... View Article

The equation of the pair of straight lines parallel to x-axis and touching the circle x² + y² – 6x – 4y – 12 = 0

1) y2 – 4y – 21 = 0 2) y2 + 4y – 21 = 0 3) y2 – 4y + 21 = 0 4) y2 + 4y + 21 = 0 Solution: The equation of the line parallel to x-axis is y =... View Article

The angle between the lines joining the points of intersection of line y = 3x + 2 and the curve x² + 2xy + 3y² + 4x + 8y – 11 = 0 to the origin, is

1) tan-1(3/2√2) 2) tan-1(2√2/3) 3) tan-1(√3) 4) tan-1(2√2) Solution: Equation of the curve is x2 + 2xy + 3y2 + 4x + 8y - 11 = 0 ..(i) Given... View Article

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Archives

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

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

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

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

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

The graph of y = |x| consists of a pair of straight lines lying

The area enclosed by the pair of lines xy = 0, the line x – 4 = 0 and y + 5 = 0 is

The equation of the pair of straight lines parallel to x-axis and touching the circle x² + y² – 6x – 4y – 12 = 0

The angle between the lines joining the points of intersection of line y = 3x + 2 and the curve x² + 2xy + 3y² + 4x + 8y – 11 = 0 to the origin, is

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