If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
True
The points A \((-2,1)\), B \((0,5)\), C \((-1,2)\) are collinear.
False
Equation of the line passing through the point \((a\cos^3\theta, a\sin^3\theta)\) and perpendicular to the line \(x \sec\theta + y \csc\theta = a\) is \(x \cos\theta - y \sin\theta = a \sin 2\theta\).
False
The straight line \(5x + 4y = 0\) passes through the point of intersection of the straight lines \(x + 2y - 10 = 0\) and \(2x + y + 5 = 0\).
True
The vertex of an equilateral triangle is \((2,3)\) and the equation of the opposite side is \(x + y = 2\). Then the other two sides are \(y - 3 = (2 \pm \sqrt{3})(x - 2)\).
True
The equation of the line joining the point \((3,5)\) to the point of intersection of the lines \(4x + y - 1 = 0\) and \(7x - 3y - 35 = 0\) is equidistant from the points \((0,0)\) and \((8,34)\).
True
The line \(\dfrac{x}{a} + \dfrac{y}{b} = 1\) moves in such a way that \(\dfrac{1}{a^2} + \dfrac{1}{b^2} = \dfrac{1}{c^2}\), where \(c\) is a constant. The locus of the foot of the perpendicular from the origin on the given line is \(x^2 + y^2 = c^2\).
True
The lines \(ax + 2y + 1 = 0\), \(bx + 3y + 1 = 0\) and \(cx + 4y + 1 = 0\) are concurrent if \(a, b, c\) are in G.P.
False
Line joining the points \((3,-4)\) and \((-2,6)\) is perpendicular to the line joining the points \((-3,6)\) and \((9,-18)\).
False