Mathematics : Straight Lines

If a point P moves such that its distances from the point A (1, 1) and the line x + y + 2 = 0 are equal, then the locus of P is

• a straight line

• a pair of straight lines

• a parabola

• an ellipse

The area (in square units) of the triangle formed by the lines x = 0, y = 0 and 3x + 4y = 12, is

• 3

• 4

• 6

• 12

The equation of the straight line perpendicular to 5x - 2y = 7 and passing through the point ofintersection of the lines 2x + 3y = 1 and 3x + 4y = 6 is

• 2x + 5y + 17 = 0

• 2x + 5y - 17 = 0

• 2x - 5y + 17 = 0

• 2x - 5y = 17

The product of the perpendicular distances from the origin on the pair of straight lines 12x² + 25xy + 12y² + 10x + 11y + 2 = 0, is

• $\frac{1}{25}$

• $\frac{2}{25}$

• $\frac{3}{25}$

• $\frac{4}{25}$

The point collinear with (1, - 2, - 3) and (2, 0, 0) among the following is

• (0, 4, 6)
  
  

• (0, - 4, - 5)

• (0, - 4, - 6)

• (0, - 4, 6)

The area of the triangle formed by the pair ofstraight lines (ax + by)² - 3(bx - ay)² = 0 and ax + by + c = 0 is

• $\frac{{\mathrm{c}}^2}{{\mathrm{a}}^2 + {\mathrm{b}}^2}$

• $\frac{{\mathrm{c}}^2}{2\left({\mathrm{a}}^2 + {\mathrm{b}}^2\right)}$

• $\frac{{\mathrm{c}}^2}{\sqrt{2}\left({\mathrm{a}}^2 + {\mathrm{b}}^2\right)}$

• $\frac{{\mathrm{c}}^2}{\sqrt{3}{\left({\mathrm{a}}^2 + {\mathrm{b}}^2\right)}^2}$

The lines x - y - 2 = 0, x + y - 4 = 0 and x + 3y = 6 meet in the common point :

• (1, 2)

• (2, 2)

• (3, 1)

• (1, 1)

The equation of the line passing through the point of intersection of the lines x - 3y + 2 = 0 and 2x + 5y - 7 = 0 and perpendicular to the line 3x + 2y + 5 = 0 is :

• 2x - 3y + 1 = 0

• 6x - 9y + 11 = 0

• 2x - 3y + 5 = 0 

• 3x - 2y + 1 = 0

The lines represented by the equation x² - y² - x + 3y - 2 = 0 are :

• x + y - 1 = 0, x - y + 2 = 0

• x - y - 2 = 0, x + y + 1 = 0

• x + y + 2 = 0, x - y - 1 = 0

• x + y - 1 = 0, x + y - 2 = 0

The centroid of the triangle formed by the pair of straight lines 12x² - 20xy + 7y² = 0 and the line 2x - 3y + 4 = 0 is :

• $\left(- \frac{7}{3}, \frac{7}{3}\right)$

• $\left(- \frac{8}{3}, \frac{8}{3}\right)$

• $\left(\frac{8}{3}, \frac{8}{3}\right)$

• $\left(\frac{4}{3}, \frac{4}{3}\right)$