Parabola questions
264 published questions with worked solutions.
- If the tangents to the parabola y^2 = 4ax at (x_1, y_1), (x_2, y_2) cut at (x_3, y_3) then
- The equation of a locus is y^2 + 2ax + 2by + c = 0. Then
- A tangent to the parabola y^2 = 4ax is inclined at 3 with the axis of the parabola. The point of contact is
- A chord PP′ of a parabola cuts the axis of the parabola at O. The feet of the perpendiculars from P and P′ on the axis are M and...
- The equation of a common tangent to the parabola y^2 = 2x and the circle x^2 + y^2 + 4x = 0 is
- Let there be two parabolas with the same axis, focus of each being exterior to the other and the latus recta being 4a and 4b. The...
- P is a point which moves in the x-y plane such that the point P is nearer to the centre of a square than any of the sides. The...
- P(2, 2) and Q ( 12, -1 ) are two points on the parabola y^ 2 = 2x. The coordinates of the point R on the parabola, where the...
- Let the parabolas y = x^ 2 + ax + b and y = x(c - x) touch each other at the point (1, 0). Then
- Let y = f(x) be the equation of a parabola which is touched by the line y = x at the point where x = 1. Then
- If the latus rectum of the parabola 2x^ 2 -ky+3=0 be 2 then the vertex is
- If y=2 be the directrix and (0,1) be the vertex of the parabola x^ 2 + y+ =0 then ( , ) is equal to
- If P_r=(x_r,y_r); r=1,2,3; are three points on the parabola x^ 2 =8y, where x_1,x_2,x_3 are in GP, then y_1,y_2,y_3 are in
- If the angle between the tangents from the point ( ,1) to the parabola y^2=16x be 2 then is
- A focal chord of the parabola y^2=16x touches the circle (x-6)^2+y^2=2. Then the possible values of the slope of the chord are
- x^2+2( -1)xy+y^2+3x+5y+1=0 is the equation of Column I: (i) a circle if is (ii) a parabola if is (iii) an ellipse if is (iv) a...
- Tangents to the parabola y^2=4x at the points P and Q meet at R(-1,0). Then Column I: (i) the length of the chord PQ is (ii) the...
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- In the parabola y^2+4=4x, a chord passing through the point (2,0) cuts the parabola at P and Q. If P=(5,4) and the tangents at P...
- y^2 = 4x is a curve and P, Q, R are three points on it where P = (1, 2), Q = ( 14, 1 ) and the tangent to the curve at R is...
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration