Parabola questions
264 published questions with worked solutions.
- Let A_1, B_1, C_1 be three points in the xy-plane. Suppose that the lines A_1C_1 and B_1C_1 are tangents to the curve y^2 = 8x at...
- A normal with slope 1 6 is drawn from the point (0, - ) to the parabola x^2 = -4ay, where a > 0. Let L be the line passing...
- If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is x + y = a, is 16, then...
- Let P(a, b) be a point on the parabola y^ 2 = 8x such that the tangent at P passes through the centre of the circle x^ 2 + y^ 2 -...
- A circle of radius 2 unit passes through the vertex and the focus of the parabola y^ 2 = 2x and touches the parabola y = (x -...
- Two tangent lines l_ 1 and l_ 2 are drawn from the point (2, 0) to the parabola 2y^ 2 = −x. If the lines l_ 1 and l_ 2 are also...
- If vertex of a parabola is (2, −1) and the equation of its directrix is 4x − 3y = 21, then the length of its latus rectum is :
- Let the focal chord of the parabola P : y^ 2 = 4x along the line L : y = mx + c, m > 0 meet the parabola at the points M and N....
- Let P : y^ 2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of /4 with the line y = 3x...
- Let PQ be a focal chord of the parabola y^ 2 = 4x such that it subtends an angle of /2 at the point (3, 0). Let the line segment...
- Let S denote the locus of the mid-points of those chords of the parabola y^2 = x, such that the area of the region enclosed...
- Let the tangent to the curve x^2+2x-4y+9=0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and...
- The ordinates of the points P and Q on the parabola with focus (3, 0) and directrix x = –3 are in the ratio 3 : 1. If R( , ) is...
- Let R be the focus of the parabola y^2=20x and the line y = mx + c intersect the parabola at two points P and Q. Let the points...
- Let the tangent to the parabola y^2=12x at the point (3, ) be perpendicular to the line 2x+2y=3. Then the square of distance of...
- Let PQ be a focal chord of the parabola y^2=36x of length 100, making an acute angle with the positive x-axis. Let the ordinate...
- Let a tangent to the curve y^2=24x meet the curve xy=2 at the points A and B. Then the mid points of such line segments AB lie on...
- The equations of two sides of a variable triangle are x = 0 and y = 3, and its third side is a tangent to the parabola y^2=6x....
- The distance of the point (6, –2 2) from the common tangent y = mx + c, m > 0, of the curves x = 2y^2 and x = 1 + y^2 is
- If the tangent at a point P on the parabola y^2=3x is parallel to the line x + 2y = 1 and the tangents at the points Q and R on...
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