A point moves so that its distance from the point (-1, 0) is always three times its distance from the point (0, 2). Find its locus.

For what value of \(\lambda \) are the three lines 2x-5y+3 = 0, 5x-9y+\(\lambda \)=0 and x-2y+1=0 are concurrent?

Find the value of k if the straight line 2x + 3y + 4 + k(6x - y + 12) = 0 is perpendicular to the line 7x + 5y - 4 = 0

For what value of k does 12x² + 7xy + ky² + 13x - y + 3 = 0 represents a pair of straight lines?

Find the equation of a circle of radius 5 whose centre lies on X-axis and passes through the point (2, 3).