Find the equation of the parabola that satisfies the following conditions: Focus\( (0, -3);\) directrix \(y = 3\)
Prove that (sin 3x+sin x) sinx+(cos 3x–cos x) cos x=0
Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(y^2 = 10x\)
(a) 2 ,\(2\sqrt{2}\) , 4 ,.... is 128 ?
(b) \(\sqrt{3}\), 3, \(3\sqrt{3}\),... is 729 ?
(c) \(\frac{1}{3},\frac{1}{9},\frac{1}{27}\) ,.... is \(\frac{1}{19683}\) ?
Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(y^2 = 12x\).
Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(x^2 = - 16y\)
Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(x^2 = 6y\)
Does the point \((-2.5, 3.5)\) lie inside, outside, or on the circle \(x^2 + y^2 = 25\) ?
Find the equation of a circle with center (2, 2) and passes through the point (4, 5).
Find equation of the line through the point (0, 2) making an angle \(\frac{2\pi}{3}\) with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
Find the equation of the circle passing through \( (0, 0)\) and making intercepts \(a\) and \(b\) on the coordinate axes.
Find the equation of the circle with radius \(5\) whose center lies on the x-axis and passes through the point \((2, 3).\)