PrepWiser › Learn › Mathematics › ParabolaParabola — JEE Main PYQs & Practice Questions Parabola is a Mathematics chapter in the JEE Main syllabus. This page brings together 104 previous-year and practice questions on Parabola, organised into 5 topics: Standard Forms, Parametric Form, Tangent and Normal, Chord of Contact and Focal Chord. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Standard Forms Let the shortest distance from (a, 0), a>0, to the parabola y²=4 x be 4 . Then the… Let P₁ be a parabola with vertex (3, 2) and focus (4, 4) and P₂ be its mirror image with… The radius of the smallest circle which touches the parabolas y=x²+2 and x=y²+2 is If the equation of the parabola with vertex V(3/2, 3) and the directrix x+2 y=0 is α… The locus of a point which divides the line segment joining the point (0, –1) and a… Let P be a variable point on the parabola y = 4x² + 1. Then, the locus of the mid-point… The length of the latus rectum of a parabola, whose vertex and focus are on the positive… Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the… If P(h, k) be a point on the parabola x=4 y², which is nearest to the point Q(0,33)… Let A(0,1), B(1,1) and C(1,0) be the mid-points of the sides of a triangle with incentre… The parabolas : a x²+2 b x+c y=0 and d x²+2 e x+f y=0 intersect on the line y=1. If a… If vertex of a parabola is (2, -1) and the equation of its directrix is 4x - 3y = 21… Let P be the parabola, whose focus is (-2,1) and directrix is 2 x+y+2=0. Then the sum of… Let a conic C pass through the point (4,-2) and P(x, y), x ≥ 3, be any point on C. Let… Let the parabola y=x²+p x-3, meet the coordinate axes at the points P, Q and R . If the… The axis of a parabola is the line y=x and its vertex and focus are in the first… Let A and B be the two points of intersection of the line y+5=0 and the mirror image of… Let the hyperbola H: x²/a²-y²/b²=1 pass through the point (2 √2,-2 √2). A parabola is… If the equation of the parabola, whose vertex is at (5, 4) and the directrix is 3x + y -… Let P Q be a chord of the parabola y²=12 x and the midpoint of P Q be at (4,1). Then… Parametric Form If the chord joining the points P₁(x₁,y₁) and P₂(x₂,y₂) on the parabola y²=12x subtends… Let A, B and C be three points on the parabola y²=6 x and let the line segment A B meet… Let O be the vertex of the parabola y²=4x and its chords OP and OQ are perpendicular to… Let R be the focus of the parabola y²=20 x and the line y=m x+c intersect the parabola… Let the parabola y=x²+px+q passing through the point (1,-1) be such that the distance… Let P(α, β) be a point on the parabola y²=4 x. If P also lies on the chord of the… Let x = 2t, y = t²/3 be a conic. Let S be the focus and B be the point on the axis of… Let A,B and C be the vertices of a variable right angled triangle inscribed in the… Let the locus of the mid-point of the chord through the origin O of the parabola y²=4x… Let P be a point on the parabola, y² = 12x and N be the foot of the perpendicular drawn… Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ red, 4 black balls… An equilateral triangle OAB is inscribed in the parabola y²=4x with the vertex O at the… If the line 3 x-2 y+12=0 intersects the parabola 4 y=3 x² at the points A and B, then at… Let A be the focus of the parabola y²=8x. Let the line y=mx+c intersect the parabola at… Let chord PQ of length 3√13 of the parabola y²=12x be such that the ordinates of points… The area (in sq. units) of an equilateral triangle inscribed in the parabola y² = 8x… The locus of the mid-point of the line segment joining the focus of the parabola y² =… Let y²=12x be the parabola with its vertex at O. Let P be a point on the parabola and A… Consider the circle C: x²+y²=4 and the parabola P: y²=8 x. If the set of all values of… Let the image of parabola x²=4y, in the line x-y=1 be (y+a)²=b(x-c), a,b,c∈ N. Then… Tangent and Normal If the three normals drawn to the parabola, y² = 2x pass through the point (a, 0) a ≠ 0… Let L₁ be a tangent to the parabola y² = 4(x + 1) and L₂ be a tangent to the parabola y²… The equation of a common tangent to the parabolas y=x² and y=-(x-2)² is Let S be the set of all a ∈ N such that the area of the triangle formed by the tangent… A tangent line L is drawn at the point (2, -4) on the parabola y² = 8x. If the line L is… The shortest distance between the line x - y = 1 and the curve x² = 2y is : Let the tangent to the parabola S : y² = 2x at the point P(2, 2) meet the x-axis at Q… For which of the following curves, the line x + √3 y = 2√3 is the tangent at the point (… Two tangent lines l₁ and l₂ are drawn from the point (2,0) to the parabola 2 y²=-x. If… Let C be the locus of the mirror image of a point on the parabola y² = 4x with respect… Let C be the circle of minimum area touching the parabola y=6-x² and the lines y=√3|x|… Let a tangent to the curve y²=24x meet the curve xy = 2 at the points A and B. Then the… Let L₁, L₂ be the lines passing through the point P(0,1) and touching the parabola 9… Let a common tangent to the curves y² = 4x and (x - 4)² + y² = 16 touch the curves at… Let the normal at the point on the parabola y² = 6x pass through the point (5, -8). If… The tangents at the points A(1,3) and B(1,-1) on the parabola y²-2 x-2 y=1 meet at the… The ordinates of the points P and Q on the parabola with focus (3,0) and directrix x=-3… The distance of the point (6,-2√2) from the common tangent y=mx+c,m > 0, of the curves… A tangent and a normal are drawn at the point P(2, -4) on the parabola y² = 8x, which… A line passing through the point A(-2,0), touches the parabola P: y²=x-2 at the point B… Chord of Contact Focal Chord Let P(4,4 √3) be a point on the parabola y²=4 a x and PQ be a focal chord of the… Let one end of a focal chord of the parabola y²=16x be (16,16). If P(α, β) divides this… If one end of a focal chord AB of the parabola y² = 8x is at A( 1/2, - 2 ), then the… Let PQ be a focal chord of the parabola y²=36 x of length 100 , making an acute angle… If the x-intercept of a focal chord of the parabola y²=8x+4y+4 is 3, then the length of… Suppose AB is a focal chord of the parabola y²=12 x of length l and slope m<√3. If the… Let the directrix of the parabola P:y²=8x, cut x-axis at the point A . Let B(α,β),α>1… Let PQ be a focal chord of length 6.25 units of the parabola y² = 4x. If O is the vertex… Let the focal chord of the parabola P: y²=4 x along the line L: y=m x+c, m>0 meet the… Let y²=12 x be the parabola and S be its focus. Let P Q be a focal chord of the parabola… Let y = mx + c, m > 0 be the focal chord of y² = - 64x, which is tangent to (x + 10)² +… Let the focal chord PQ of the parabola y²=4 x make an angle of 60° with the positive x… Let the length of the focal chord PQ of the parabola y²=12 x be 15 units. If the… Let the point P of the focal chord PQ of the parabola y²=16 x be (1,-4). If the focus of… More Mathematics chapters Frequently asked questions How many Parabola questions are there for JEE Main? PrepWiser has 104 Parabola questions for JEE Main, grouped into 5 topics such as Standard Forms, Parametric Form and Tangent and Normal.
Are these Parabola questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Parabola questions? Open any Parabola question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.